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Special function defined by an integral
In mathematics, the logarithmic integral function or integral logarithm li(x) is a special function. It is relevant in problems of physics and has number
Logarithmic_integral_function
Special function defined by an integral
exponential integral E i {\displaystyle \mathrm {Ei} } is a special function on the complex plane. It is defined as one particular definite integral of the
Exponential_integral
a list of integrals (antiderivative functions) of logarithmic functions. For a complete list of integral functions, see list of integrals. Note: x >
List of integrals of logarithmic functions
List_of_integrals_of_logarithmic_functions
Mathematical operation in calculus
mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula f ′ f {\displaystyle {\frac {f'}{f}}}
Logarithmic_derivative
Special function defined by an integral
mathematics, trigonometric integrals are a family of nonelementary integrals involving trigonometric functions. The different sine integral definitions are Si
Trigonometric_integral
Mathematical function, inverse of an exponential function
of x. A far better estimate of π(x) is given by the offset logarithmic integral function Li(x), defined by L i ( x ) = ∫ 2 x 1 ln ( t ) d t . {\displaystyle
Logarithm
Integrals not expressible in closed-form from elementary functions
(elliptic integral) 1 ln x {\displaystyle {\frac {1}{\ln x}}} (logarithmic integral) e − x 2 {\displaystyle e^{-x^{2}}} (error function, Gaussian integral) sin
Nonelementary_integral
Indefinite integral
function, primitive integral or indefinite integral of a function f is a differentiable function F whose derivative is equal to the original function
Antiderivative
functions List of integrals of exponential functions List of integrals of logarithmic functions List of integrals of Gaussian functions Gradshteyn, Ryzhik
Lists_of_integrals
Mathematical function
\pi } denotes the prime counting function, Li {\displaystyle \operatorname {Li} } the logarithmic integral function with inverse Li − 1 {\displaystyle
Landau's_function
Extension of the factorial function
The gamma function then is defined in the complex plane as the analytic continuation of this integral function: it is a meromorphic function which is holomorphic
Gamma_function
Mathematical constant
mathematical constant defined as the unique positive zero of the logarithmic integral function. It is named after Srinivasa Ramanujan and Johann Georg von
Ramanujan–Soldner_constant
Operation in mathematical calculus
below are negative. Integrals also refer to the concept of an antiderivative, a function whose derivative is the given function; in this case, they are
Integral
Large number used in number theory
{\displaystyle x} for which the prime-counting function π ( x ) {\displaystyle \pi (x)} exceeds the logarithmic integral function li ( x ) . {\displaystyle \operatorname
Skewes's_number
Functions of an angle
trigonometric functions were often combined with logarithms in compound functions like the logarithmic sine, logarithmic cosine, logarithmic secant, logarithmic cosecant
Trigonometric_functions
Function representing the number of primes less than or equal to a given number
\left(x^{1/n}\right),} μ(n) is the Möbius function, li(x) is the logarithmic integral function, ρ indexes every zero of the Riemann zeta function, and li(xρ/n) is not
Prime-counting_function
Integral of sin(x)/x from 0 to infinity
as the sine integral, an antiderivative of the sinc function, is not an elementary function. In this case, the improper definite integral can be determined
Dirichlet_integral
Logarithm to the base of the mathematical constant e
logarithmic identities Logarithm of a matrix Logarithmic coordinates of an element of a Lie group. Logarithmic differentiation Logarithmic integral function
Natural_logarithm
Inverse functions of sin, cos, tan, etc.
argument of the arcosh function creates a negative half of its graph, making it identical to the signum logarithmic function shown above. All of these
Inverse trigonometric functions
Inverse_trigonometric_functions
Characterization of how many integers are prime
Gustav Lejeune Dirichlet came up with his own approximating function, the logarithmic integral li(x) (under the slightly different form of a series, which
Prime_number_theorem
Family of solutions to related differential equations
\psi (z)} is the digamma function, the logarithmic derivative of the gamma function. There is also a corresponding integral formula (for Re(x) > 0): Y
Bessel_function
Mathematical function
elementary but lack elementary antiderivatives; the integral of the Gaussian function is the error function: ∫ exp ( − x 2 ) d x = π 2 erf x + C . {\displaystyle
Gaussian_function
Mathematical function
In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function: ψ ( z ) = d d z ln Γ ( z ) = Γ ′ ( z ) Γ ( z )
Digamma_function
List of integrals of exponential functions List of integrals of logarithmic functions List of integrals of area functions Partial derivative Disk integration
List_of_calculus_topics
Integration over a non-flat region in 3D space
integral analogue of the line integral. Given a surface, one may integrate over this surface a scalar field (that is, a function of position which returns
Surface_integral
{\displaystyle n} Radical function: The product of the distinct prime factors of a positive integer input. Logarithmic integral function: Integral of the reciprocal
List of mathematical functions
List_of_mathematical_functions
Mathematical concept
function li occurring in the first term is the (unoffset) logarithmic integral function given by the Cauchy principal value of the divergent integral
Explicit formulae for L-functions
Explicit_formulae_for_L-functions
Antiderivative of the secant function
In calculus, the integral of the secant function can be evaluated using a variety of methods and there are multiple ways of expressing the antiderivative
Integral of the secant function
Integral_of_the_secant_function
Method of evaluating certain integrals along paths in the complex plane
of evaluating certain integrals along paths in the complex plane. Contour integration is used to study complex-valued functions that are holomorphic in
Contour_integration
Conjecture on zeros of the zeta function
imaginary part. The function li {\displaystyle \operatorname {li} } occurring in the first term is the (unoffset) logarithmic integral function given by the
Riemann_hypothesis
Method of mathematical integration
the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that function and
Lebesgue_integral
Transcendental single-variable function
particularly in relation to the evaluation of many classes of logarithmic and polylogarithmic integrals, both definite and indefinite. They also have numerous
Clausen_function
Elementary functions and their finitely iterated integrals
extraction) and antiderivatives. The logarithmic function does not need to be explicitly included since it is the integral of 1 / x {\displaystyle 1/x} . It
Liouvillian_function
Conditions for switching order of integration in calculus
a function is Lebesgue integrable on a rectangle X × Y {\displaystyle X\times Y} , then one can evaluate the double integral as an iterated integral: ∬
Fubini's_theorem
offset logarithmic integral function. li – logarithmic integral function or linearly independent. lim – limit of a sequence, or of a function. lim inf
List of mathematical abbreviations
List_of_mathematical_abbreviations
List of formulae involving π – Uses of the constant List of integrals of logarithmic functions List of mathematical identities Lists of mathematics topics
List of logarithmic identities
List_of_logarithmic_identities
Special mathematical function
polylogarithmic functions, nor with the offset logarithmic integral Li(z), which has the same notation without the subscript. Different polylogarithm functions in
Polylogarithm
Analytic function in mathematics
ISBN 0-387-98308-2. Raoh, Guo (1996). "The distribution of the logarithmic derivative of the Riemann zeta function". Proceedings of the London Mathematical Society
Riemann_zeta_function
Provides an asymptotic formula for counting the number of prime ideals of a number field
Theorem, a more precise estimate may be given in terms of the logarithmic integral function. The number of prime ideals of norm ≤ X is L i ( X ) + O K (
Landau_prime_ideal_theorem
Differentiation under the integral sign formula
b(x)<\infty } and the integrands are functions dependent on x , {\displaystyle x,} the derivative of this integral is expressible as d d x ( ∫ a ( x )
Leibniz_integral_rule
Type of mathematical function
including the exponential integral (Ei) logarithmic integral (Li or li) and Fresnel integrals (S and C) the error function, e r f ( x ) = 2 π ∫ 0 x
Elementary_function
Definite integral of a scalar or vector field along a path
mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms path integral, curve integral, and curvilinear
Line_integral
Topics referred to by the same term
domain (ccTLD) for Liechtenstein Li, the polylogarithm function Li, the logarithmic integral function <li></li>, indicating an item in an HTML list; see HTML
Li
Difference of two numbers divided by the logarithm of their quotient
In mathematics, the logarithmic mean is a function of two non-negative numbers which is equal to their difference divided by the logarithm of their quotient
Logarithmic_mean
Measure for evaluating probabilistic forecasts
probability density function f : R n → R + {\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} _{+}} . The multivariate logarithmic score is similar to the
Scoring_rule
Topics referred to by the same term
The term integral logarithm may stand for: Discrete logarithm in algebra, Logarithmic integral function in calculus. This disambiguation page lists articles
Integral_logarithm
Theorem in complex analysis
poles of a meromorphic function to a contour integral of the function's logarithmic derivative. If f is a meromorphic function inside and on some closed
Argument_principle
Branch of mathematics
differential calculus and integral calculus. Differential calculus studies instantaneous rates of change and slopes of curves; integral calculus studies accumulation
Calculus
Method of mathematical differentiation
calculus, logarithmic differentiation or differentiation by taking logarithms is a method used to differentiate functions by employing the logarithmic derivative
Logarithmic_differentiation
list of integrals of exponential functions. For a complete list of integral functions, please see the list of integrals. Indefinite integrals are antiderivative
List of integrals of exponential functions
List_of_integrals_of_exponential_functions
Rules for computing derivatives of functions
{df_{i}}{dx}}{\text{ exists.}}} The logarithmic derivative is another way of stating the rule for differentiating the logarithm of a function (using the chain rule):
Differentiation_rules
Formula for the derivative of a ratio of functions
\end{aligned}}} Taking the absolute value of the functions is necessary for the logarithmic differentiation of functions that may have negative values, as logarithms
Quotient_rule
Method of calculating heat transfer in flow systems
In thermal engineering, the logarithmic mean temperature difference (LMTD) is used to determine the temperature driving force for heat transfer in flow
Logarithmic mean temperature difference
Logarithmic_mean_temperature_difference
Concept in mathematical analysis
a real-valued function of a single variable integrated in the sense of Riemann (or Darboux) over a single interval, improper integrals may be in any of
Improper_integral
Number, approximately 3.14
transform. This is the integral transform, that takes a complex-valued integrable function f on the real line to the function defined as: f ^ ( ξ ) =
Pi
Basic integral in elementary calculus
analysis, the Riemann integral is a rigorous definition of the integral of a function on an interval. It defines the integral by approximating the region
Riemann_integral
Mathematical transform that expresses a function of time as a function of frequency
mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function that describes the extent to which various
Fourier_transform
Integral over a 3-D domain
densities, or to calculate mass from a corresponding density function. Often the volume integral is represented in terms of a differential volume element
Volume_integral
Point of interest for complex multi-valued functions
multiple-valued function and, in an appropriate sense, is continuous at the origin. This is in contrast to transcendental and logarithmic branch points
Branch_point
Mathematical function having a characteristic S-shaped curve or sigmoid curve
distribution functions (which go from 0 to 1), such as the integrals of the logistic density, the normal density, and Student's t probability density functions. The
Sigmoid_function
Mathematical function
\operatorname {am} (u|m)} is a multivalued function (in u {\displaystyle u} ) with infinitely many logarithmic branch points (the branches differ by integer
Jacobi_elliptic_functions
Matrix of partial derivatives of a vector-valued function
variables in multiple integrals. Let f : R n → R m {\textstyle \mathbf {f} :\mathbb {R} ^{n}\to \mathbb {R} ^{m}} be a function such that each of its
Jacobian matrix and determinant
Jacobian_matrix_and_determinant
Complex-differentiable (mathematical) function
v(x,y)} is holomorphic. Cauchy's integral theorem implies that the contour integral of every holomorphic function along a loop vanishes: ∮ γ f ( z )
Holomorphic_function
1 minus the cosine of an angle
the single angle (θ = 0, 2π, …) where it is zero—thus, one could use logarithmic tables for multiplications in formulas involving versines. In fact, the
Versine
Generalization of definite integrals to functions of multiple variables
multiple integral is a definite integral of a function of several real variables, for instance, f(x, y) or f(x, y, z). Integrals of a function of two variables
Multiple_integral
Mathematical function with no sudden changes
a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function. This implies
Continuous_function
Special function related to the dilogarithm
The inverse tangent integral is a special function, defined by: Ti 2 ( x ) = ∫ 0 x arctan t t d t {\displaystyle \operatorname {Ti} _{2}(x)=\int _{0}^{x}{\frac
Inverse_tangent_integral
S-shaped curve
"logarithmic" to "logistic" transition first noted by Pierre-François Verhulst, as noted above) and then reaching a maximal limit. A logistic function
Logistic_function
2D graphic with logarithmic scales on both axes
two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Power functions – relationships of the form y = a x k
Log–log_plot
Concept of complex analysis
powerful tool to evaluate line integrals of analytic functions over closed curves; it can often be used to compute real integrals and infinite series as well
Residue_theorem
Relationship between derivatives and integrals
states that for a continuous function f , an antiderivative or indefinite integral F can be obtained as the integral of f over an interval with a variable
Fundamental theorem of calculus
Fundamental_theorem_of_calculus
Integral using products instead of sums
systems of linear differential equations. The classical Riemann integral of a function f : [ a , b ] → R {\displaystyle f:[a,b]\to \mathbb {R} } can be
Product_integral
Risk measure estimating the average loss in the worst tail of the distribution
incomplete gamma function, l i ( x ) = ∫ d x ln x {\displaystyle \mathrm {li} (x)=\int {\frac {dx}{\ln x}}} is the logarithmic integral function. If the loss
Expected_shortfall
Method for evaluating indefinite integrals
the logarithmic part of a mixed transcendental-algebraic integral by Brian L. Miller. The Risch algorithm is used to integrate elementary functions. These
Risch_algorithm
Mathematical theorem, used in calculus
In mathematics, integrals of inverse functions can be computed by means of a formula that expresses the antiderivatives of the inverse f − 1 {\displaystyle
Integral_of_inverse_functions
Astronomical measure
magnitude system is logarithmic, the power law has logarithmic slope α + 1 {\displaystyle \alpha +1} . This is why a Schechter function with α = − 1 {\displaystyle
Luminosity function (astronomy)
Luminosity_function_(astronomy)
Calculus on stochastic processes
disciplines). The Stratonovich integral can readily be expressed in terms of the Itô integral, and vice versa. Stochastic integrals do NOT obey the usual chain
Stochastic_calculus
Instantaneous rate of change (mathematics)
antiderivative of a function gives a way to compute the areas of shapes bounded by that function. More precisely, the integral of a function over a closed interval
Derivative
Point to which functions converge in analysis
mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input which
Limit_of_a_function
Term used in the theories of Riemann surfaces and algebraic curves
Weierstrass zeta function was called an integral of the second kind in elliptic function theory; it is a logarithmic derivative of a theta function, and therefore
Differential of the first kind
Differential_of_the_first_kind
Mathematical method in calculus
partial integration is a process that finds the integral of a product of functions in terms of the integral of the product of their derivative and antiderivative
Integration_by_parts
Mapping involving integration between function spaces
mathematics, an integral transform is a type of transformation that maps a function from its original function space into another function space via integration
Integral_transform
Analytic function that does not satisfy a polynomial equation
mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation whose coefficients are functions of the independent variable
Transcendental_function
Meromorphic function
trivial consequence of the Bohr–Mollerup theorem for the gamma function where strictly logarithmic convexity on R + {\displaystyle \mathbb {R} ^{+}} is demanded
Polygamma_function
Extension of superfactorials to the complex numbers
exp(x) = ex is the exponential function, and Π {\displaystyle \Pi } denotes multiplication (capital pi notation). The integral representation, which may be
Barnes_G-function
Function that interpolates the factorial
we obtain uniqueness of this function, most often given by the Gamma function. The most common condition is the logarithmic convexity: this is the Bohr-Mollerup
Pseudogamma_function
Mathematical function having a characteristic "bell"-shaped curve
maximum at small x. Hence, the integral of a bell-shaped function is typically a sigmoid function. Bell shaped functions are also commonly symmetric. Many
Bell-shaped_function
Integral transform useful in probability theory, physics, and engineering
(/ləˈplɑːs/), is an integral transform that converts a function of a real variable (usually t {\displaystyle t} , in the time domain) to a function of a complex
Laplace_transform
Mathematical functions that quantify complexity
coordinates (e.g. 7 for the coordinates (3/7, 1/2)), but in a logarithmic scale. Height functions allow mathematicians to count objects, such as rational points
Height_function
Mathematical function
Re zn = −n + 1/2 quickly and their imaginary part increases slowly logarithmic with n. For example, z1 = −0.4121345... + 0.5978119...i and z2 = −1.4455692
Trigamma_function
Technique in integral evaluation
the function f ( g ( x ) ) ⋅ g ′ ( x ) {\displaystyle f(g(x))\cdot g'(x)} is also integrable on [ a , b ] {\displaystyle [a,b]} . Hence the integrals ∫
Integration_by_substitution
Relation of flow speed to wall distance
In fluid dynamics, the law of the wall (also known as the logarithmic law of the wall) states that the average velocity of a turbulent flow at a certain
Law_of_the_wall
Theorem in mathematics
mathematical analysis, the inverse function theorem gives sufficient conditions for a function to have an inverse function. The essential idea is that if
Inverse_function_theorem
Solution of a confluent hypergeometric equation
} Coulomb wave function Cunningham functions Exponential integral and related functions such as the sine integral, logarithmic integral Hermite polynomials
Confluent hypergeometric function
Confluent_hypergeometric_function
completely monotonic function, logarithmically completely monotonic function, strongly logarithmically completely monotonic function, strongly completely
Absolutely and completely monotonic functions and sequences
Absolutely_and_completely_monotonic_functions_and_sequences
Formula for the derivative of a product
Note: Taking the absolute value of the functions is necessary for the logarithmic differentiation of functions that may have negative values, as logarithms
Product_rule
Theorem in mathematics
theorem) is a theorem about differentiable functions, roughly stating that the average rate of change of such a function over an interval is equal to the instantaneous
Mean_value_theorem
Divergent sum of positive unit fractions
_{k=1}^{n}{\frac {1}{k}}.} These numbers grow very slowly, with logarithmic growth, as can be seen from the integral test. More precisely, by the Euler–Maclaurin formula
Harmonic_series_(mathematics)
Mathematical approximation of a function
tan x, sec x, ln sec x (the integral of tan), ln tan 1/2(1/2π + x) (the integral of sec, the inverse Gudermannian function), arcsec(√2 ex), and 2 arctan
Taylor_series
Mathematical functions
Christian (1978). "Fonctions elliptiques et intégrales abéliennes" [Elliptic functions and Abelian integrals]. In Dieudonné, Jean (ed.). Abrégé d'histoire
Lemniscate_elliptic_functions
LOGARITHMIC INTEGRAL-FUNCTION
LOGARITHMIC INTEGRAL-FUNCTION
Girl/Female
American, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Tamil, Telugu
Plucked Flower; Voice of Heart; Woman; Intellect; Behold of Any Beautiful Scene; Internal Beauty
Male
Celtic
, great justiciary, or functionary.
Male
Egyptian
, Functionary of the Interior.
Male
Egyptian
, the son of the functionary Heknofre.
Girl/Female
Arabic, Bengali, Gujarati, Hindu, Indian, Kannada, Marathi, Muslim, Punjabi, Sikh, Sindhi, Telugu
Heart; Inner Beauty; Fame; Internal Nature; Wisdom
Male
Egyptian
, an Egyptian functionary.
Surname or Lastname
English
English : nickname from the animal, Middle English catte ‘cat’. The word is found in similar forms in most European languages from very early times (e.g. Gaelic cath, Slavic kotu). Domestic cats were unknown in Europe in classical times, when weasels fulfilled many of their functions, for example in hunting rodents. They seem to have come from Egypt, where they were regarded as sacred animals.English : from a medieval female personal name, a short form of Catherine.Variant spelling of German and Dutch Katt.
Male
Egyptian
, a high Egyptian functionary.
Boy/Male
Indian
Internal Cleanliness
Biblical
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Male
Egyptian
, a great functionary.
Surname or Lastname
English (chiefly Kent and Sussex)
English (chiefly Kent and Sussex) : occupational name for a designer or engineer, from a Middle English reduced form of Old French engineor ‘contriver’ (a derivative of engaigne ‘cunning’, ‘ingenuity’, ‘stratagem’, ‘device’). Engineers in the Middle Ages were primarily designers and builders of military machines, although in peacetime they might turn their hands to architecture and other more pacific functions.German : from the Latin personal name Januarius (see January 1). Jänner is a South German word for ‘January’, and so it is possible that this is one of the surnames acquired from words denoting months of the year, for example by converts who had been baptized in that month, people who were born or baptized in that month, or people whose taxes were due in January.
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Surname or Lastname
English
English : occupational name for a dresser of cloth, Old English fullere (from Latin fullo, with the addition of the English agent suffix). The Middle English successor of this word had also been reinforced by Old French fouleor, foleur, of similar origin. The work of the fuller was to scour and thicken the raw cloth by beating and trampling it in water. This surname is found mostly in southeast England and East Anglia. See also Tucker and Walker.In a few cases the name may be of German origin with the same form and meaning as 1 (from Latin fullare).Americanized version of French Fournier.Samuel Fuller (1589–1633), born in Redenhall, Norfolk, England, was among the Pilgrim Fathers who sailed on the Mayflower in 1620. He was a deacon of the church and until his death functioned as Plymouth Colony’s physician.
Surname or Lastname
English and French
English and French : nickname for a handsome man (perhaps also ironically for an ugly one), from Old French beu, bel ‘fair’, ‘lovely’ (Late Latin bellus).Hungarian (Bél) : from the old secular Hungarian name Bél, or alternatively from bél ‘internal part’, probably an occupational name for a servant who worked in the household.Czech (BÄ›l) from Czech bÃlý ‘white’.
Surname or Lastname
Irish
Irish : reduced Anglicized form of either of two Gaelic names, Ó DuibhÃn ‘descendant of DuibhÃn’, a byname meaning ‘little black one’, or Ó DaimhÃn ‘descendant of DaimhÃn’, a byname meaning ‘fawn’, ‘little stag’. These are attenuated versions of Ó Dubháin and Ó Damháin, and are the phonetic origin of Anglicizations with an internal v (as opposed to w, as in Dewan, or monosyllabic forms with an o or u) (see Doane).English and French : nickname, of literal or ironic application, from Middle English, Old French devin, divin ‘excellent’, ‘perfect’ (Latin divinus ‘divine’).
Surname or Lastname
English
English : topographic name for someone who lived by the gates of a medieval walled town. The Middle English singular gate is from the Old English plural, gatu, of geat ‘gate’ (see Yates). Since medieval gates were normally arranged in pairs, fastened in the center, the Old English plural came to function as a singular, and a new Middle English plural ending in -s was formed. In some cases the name may refer specifically to the Sussex place Eastergate (i.e. ‘eastern gate’), known also as Gates in the 13th and 14th centuries, when surnames were being acquired.Americanized spelling of German Götz (see Goetz).Translated form of French Barrière (see Barriere).In New England, Gates was the preferred English version of the name of an extensive French family, called Barrière dit Langevin.
Male
Egyptian
, an Egyptian functionary.
LOGARITHMIC INTEGRAL-FUNCTION
LOGARITHMIC INTEGRAL-FUNCTION
Boy/Male
Hindu, Indian
Related to God Vishnu
Male
German
Old German name, GOMERIC means "man-power."
Boy/Male
English American German
Brave; powerful.
Female
Spanish
Spanish pet form of Greek Eva, EVITA means "life."
Girl/Female
Irish
Ancient.
Biblical
the perfection of Jehovah
Boy/Male
Indian, Punjabi, Sikh
One who Reflects on God
Girl/Female
Hindu, Indian, Marathi
The Best Voice; Melody
Boy/Male
Arabic, Hindu, Indian, Kannada, Marathi, Muslim, Telugu
Chosen
Girl/Female
African, Arabic, Australian, Finnish, German, Greek, Japanese, Swahili, Turkish
To Speak; Omen; A Sign from the Heaven; Divine Omen
LOGARITHMIC INTEGRAL-FUNCTION
LOGARITHMIC INTEGRAL-FUNCTION
LOGARITHMIC INTEGRAL-FUNCTION
LOGARITHMIC INTEGRAL-FUNCTION
LOGARITHMIC INTEGRAL-FUNCTION
v. t.
To subject to the operation of integration; to find the integral of.
n.
A space between things; a void space intervening between any two objects; as, an interval between two houses or hills.
n.
A brief space of time between the recurrence of similar conditions or states; as, the interval between paroxysms of pain; intervals of sanity or delirium.
n.
The number corresponding to a logarithm. The word has been sometimes, though rarely, used to denote the complement of a given logarithm; also the logarithmic cosine corresponding to a given logarithmic sine.
n.
A whole; an entire thing; a whole number; an individual.
a.
Essential to completeness; constituent, as a part; pertaining to, or serving to form, an integer; integrant.
adv.
In an integral manner; wholly; completely; also, by integration.
a.
Derived from, or dependent on, the thing itself; inherent; as, the internal evidence of the divine origin of the Scriptures.
a.
Inward; interior; being within any limit or surface; inclosed; -- opposed to external; as, the internal parts of a body, or of the earth.
a.
Making part of a whole; necessary to constitute an entire thing; integral.
n.
The decimal part of a logarithm, as distinguished from the integral part, or characteristic.
a.
See Logarithmic.
a.
Pertaining to its own affairs or interests; especially, (said of a country) domestic, as opposed to foreign; as, internal trade; internal troubles or war.
a.
Pertaining to, or proceeding by, integration; as, the integral calculus.
adv.
By the use of logarithms.
n.
Space of time between any two points or events; as, the interval between the death of Charles I. of England, and the accession of Charles II.
a.
Alt. of Logarithmical
n.
The integral part (whether positive or negative) of a logarithm.
a.
Of or pertaining to logarithms; consisting of logarithms.
n.
An expression which, being differentiated, will produce a given differential. See differential Differential, and Integration. Cf. Fluent.