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Indicator function of rational numbers
In mathematics, the Dirichlet function is the indicator function 1 Q {\displaystyle \mathbf {1} _{\mathbb {Q} }} of the set of rational numbers Q {\displaystyle
Dirichlet_function
Type of mathematical function
In mathematics, a Dirichlet L-series is a function of the form L ( s , χ ) = ∑ n = 1 ∞ χ ( n ) n s , {\displaystyle L(s,\chi )=\sum _{n=1}^{\infty }{\frac
Dirichlet_L-function
Function in analytic number theory
in the area of analytic number theory, the Dirichlet eta function is defined by the following Dirichlet series, which converges for any complex number
Dirichlet_eta_function
Mathematical series
Riemann zeta function is a Dirichlet series, as are the Dirichlet L-functions. Specifically, the Riemann zeta function ζ(s) is the Dirichlet series of the
Dirichlet_series
Special mathematical function
mathematics, the Dirichlet beta function (also known as the Catalan beta function) is a special function, closely related to the Riemann zeta function. It is a
Dirichlet_beta_function
Meromorphic function on the complex plane
hypothesis and its generalisations. A Dirichlet series, usually convergent on a half-plane, that may give rise to an L-function via analytic continuation, is
L-function
German mathematician (1805–1859)
Johann Peter Gustav Lejeune Dirichlet (/ˌdɪərɪˈkleɪ/; German: [ləˈʒœn diʁiˈkleː]; 13 February 1805 – 5 May 1859) was a German mathematician. In number
Peter Gustav Lejeune Dirichlet
Peter_Gustav_Lejeune_Dirichlet
Synchrotron function Riemann zeta function: A special case of Dirichlet series. Riemann Xi function Dirichlet eta function: An allied function. Dirichlet beta
List of mathematical functions
List_of_mathematical_functions
Function that is discontinuous at rationals and continuous at irrationals
names: the popcorn function, the raindrop function, the countable cloud function, the modified Dirichlet function, the ruler function (not to be confused
Thomae's_function
Function which is not continuous at any point of its domain
indicator function of the rational numbers, also known as the Dirichlet function. This function is denoted as 1 Q {\displaystyle \mathbf {1} _{\mathbb {Q}
Nowhere_continuous_function
Complex-valued arithmetic function
a complex-valued arithmetic function χ : Z → C {\displaystyle \chi :\mathbb {Z} \rightarrow \mathbb {C} } is a Dirichlet character of modulus m {\displaystyle
Dirichlet_character
Probability distribution
In probability and statistics, the Dirichlet distribution (after Peter Gustav Lejeune Dirichlet), often denoted Dir ( α ) {\displaystyle \operatorname
Dirichlet_distribution
Formal power series
generating functions, including ordinary generating functions, exponential generating functions, Lambert series, Bell series, and Dirichlet series. Every
Generating_function
Type of constraint on solutions to differential equations
weight function w appearing in the boundary expression is termed a primary variable, and its specification constitutes the essential or Dirichlet boundary
Dirichlet_boundary_condition
Mathematical operation on arithmetical functions
In mathematics, Dirichlet convolution (or divisor convolution) is a binary operation defined for arithmetic functions; it is important in number theory
Dirichlet_convolution
Integral of sin(x)/x from 0 to infinity
the Dirichlet integral, after the German mathematician Peter Gustav Lejeune Dirichlet, one of which is the improper integral of the sinc function over
Dirichlet_integral
Function studied by Ramanujan
Sequences. 13: Article 10.7.4. Apostol, Tom M. (1990) [1976]. Modular Functions and Dirichlet Series in Number Theory. Graduate Texts in Mathematics. Vol. 41
Ramanujan_tau_function
Method of mathematical integration
continuous functions, including elementary functions, for example polynomials. However, the graphs of other functions, for example the Dirichlet function, do
Lebesgue_integral
Analytic function in mathematics
Riemann zeta function, such as Dirichlet series, Dirichlet L-functions and L-functions, are known. The Riemann zeta function ζ(s) is a function of a complex
Riemann_zeta_function
Modern application of infinitesimals
extension of the Dirichlet function takes different values (0 and 1) at these two infinitely close points, and therefore the Dirichlet function is not continuous
Nonstandard_calculus
Point to which functions converge in analysis
}}\\0&x{\text{ irrational }}\end{cases}}} (a.k.a., the Dirichlet function) has no limit at any x-coordinate. The function f ( x ) = { 1 for x < 0 2 for x ≥ 0 {\displaystyle
Limit_of_a_function
Mathematical function characterizing set membership
{1} _{A}(x)=\left[\ x\in A\ \right].} For example, the Dirichlet function is the indicator function of the rational numbers as a subset of the real numbers
Indicator_function
Function with a repeating pattern
periodic but possess properties that make them less intuitive. The Dirichlet function, for example, is periodic, with any nonzero rational number serving
Periodic_function
Functions such that f(–x) equals f(x) or –f(x)
multiplication. A function's being odd or even does not imply differentiability, or continuity. For example, the Dirichlet function is even, but is nowhere
Even_and_odd_functions
Family of stochastic processes
In probability theory, Dirichlet processes (after the distribution associated with Peter Gustav Lejeune Dirichlet) are a family of stochastic processes
Dirichlet_process
Operation in differential calculus
derivative is finite at 0, i.e. this is an essential discontinuity. The Dirichlet function, defined as: f ( x ) = { 1 , if x is rational 0 , if x is irrational
Symmetric_derivative
Mathematical measure of a function's variability
the Dirichlet energy is a measure of how variable a function is. More abstractly, it is a quadratic functional on the Sobolev space H1. The Dirichlet energy
Dirichlet_energy
Theorem on the number of primes in arithmetic sequences
In number theory, Dirichlet's theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there
Dirichlet's theorem on arithmetic progressions
Dirichlet's_theorem_on_arithmetic_progressions
Problem of solving a partial differential equation subject to prescribed boundary values
In mathematics, a Dirichlet problem asks for a function which solves a specified partial differential equation (PDE) in the interior of a given region
Dirichlet_problem
Dunkl–Cherednik operator Dickman–de Bruijn function Peter Gustav Lejeune Dirichlet: Dirichlet function, Dirichlet L-function Engel: Engel expansion Erdélyi Artúr:
List of eponyms of special functions
List_of_eponyms_of_special_functions
the characteristic function of the rational numbers, χ Q {\displaystyle \chi _{\mathbb {Q} }} , also known as the Dirichlet function which is discontinuous
Baire_function
Generalized function whose value is zero everywhere except at zero
Fourier series states that the Dirichlet kernel restricted to the interval [−π,π] tends to a multiple of the delta function as N → ∞. This is interpreted
Dirac_delta_function
Theorem
In mathematics, the Dirichlet–Jordan test gives sufficient conditions for a complex-valued, periodic function f {\displaystyle f} to be equal to the sum
Dirichlet–Jordan_test
Functions in mathematics
is Dirichlet's principle, representing harmonic functions in the Sobolev space H 1 ( {\displaystyle H^{1}(} as the minimizers of the Dirichlet energy
Harmonic_function
and rings) Dirichlet algebra Dirichlet beta function Dirichlet boundary condition (differential equations) Neumann–Dirichlet method Dirichlet characters
List of things named after Peter Gustav Lejeune Dirichlet
List_of_things_named_after_Peter_Gustav_Lejeune_Dirichlet
Concept in mathematical analysis
In mathematical analysis, the Dirichlet kernel, is the collection of periodic functions defined as D n ( x ) = ∑ k = − n n e i k x = ( 1 + 2 ∑ k = 1 n
Dirichlet_kernel
Function that attains finitely many values
is the Dirichlet function over the real line, which takes the value 1 if x is rational and 0 otherwise. (Thus the "simple" of "simple function" has a
Simple_function
Multiplicative function in number theory
function are plotted below: Larger values can be checked in: Wolframalpha the b-file of OEIS The Dirichlet series that generates the Möbius function is
Möbius_function
Mathematical function whose set of values is bounded
number (cf. Dirichlet function) is bounded. Thus, a function does not need to be "nice" in order to be bounded. The set of all bounded functions defined on
Bounded_function
Method of solution to differential equations
the electric field. If the problem is to solve a Dirichlet boundary value problem, the Green's function should be chosen such that G(x,x′) vanishes when
Green's_function
Second-order partial differential equation
solution to the corresponding Dirichlet problem. The Neumann boundary conditions for Laplace's equation specify not the function φ itself on the boundary of
Laplace's_equation
Mathematical conjecture about zeros of L-functions
are called Dedekind zeta-functions), Maass forms, and Dirichlet characters (in which case they are called Dirichlet L-functions). When the Riemann hypothesis
Generalized Riemann hypothesis
Generalized_Riemann_hypothesis
Generalization of the Riemann zeta function for algebraic number fields
of the Riemann zeta function: they can be defined as a Dirichlet series, have an analytic continuation to a meromorphic function on the complex plane
Dedekind_zeta_function
Counterintuitive mathematical object
example, the Dirichlet function is Lebesgue integrable, and convolution with test functions is used to approximate any locally integrable function by smooth
Pathological_(mathematics)
Special mathematical function defined as sin(x)/x
integrals Dirichlet integral – Integral of sin(x)/x from 0 to infinity Lanczos resampling – Technique in signal processing List of mathematical functions Shannon
Sinc_function
example, the Dirichlet function. Locally constant function: a continuous function into a discrete space. Homeomorphism: is a bijective function that is also
List_of_types_of_functions
If there are more items than boxes holding them, one box must contain at least two items
commonly called Dirichlet's box principle or Dirichlet's drawer principle after an 1834 treatment of the principle by Peter Gustav Lejeune Dirichlet under the
Pigeonhole_principle
On converting relations to functions of several real variables
In multivariable calculus, the implicit function theorem is a theorem that provides sufficient conditions under which a planar curve specified by F ( x
Implicit_function_theorem
Generative topic model
In natural language processing, latent Dirichlet allocation (LDA) is a generative statistical model that explains how a collection of text documents can
Latent_Dirichlet_allocation
Exploring properties of the integers with complex analysis
begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic progressions
Analytic_number_theory
Class of mathematical functions
1017/cbo9780511791246. ISBN 978-0-521-53429-1. Apostol, Tom M. (1976), Modular functions and Dirichlet series in number theory (in German), New York: Springer-Verlag
Weierstrass_elliptic_function
Concept in potential theory
least one function making the Dirichlet's integral finite). This concept is named after the German mathematician Peter Gustav Lejeune Dirichlet. The name
Dirichlet's_principle
Any real function on R admits a continuous restriction on a dense subset of R
Henry Blumberg. For instance, the restriction of the Dirichlet function (the indicator function of the rational numbers Q {\displaystyle \mathbb {Q} }
Blumberg_theorem
Function equal to the product of its values on coprime factors
{\displaystyle \tau (n)} : the Ramanujan tau function All Dirichlet characters are completely multiplicative functions, for example ( n / p ) {\displaystyle
Multiplicative_function
Inputs for which a function's value is non-zero
f : [ 0 , 1 ] → R {\displaystyle f:[0,1]\to \mathbb {R} } is the Dirichlet function that is 0 {\displaystyle 0} on irrational numbers and 1 {\displaystyle
Support_(mathematics)
Number of integers coprime to and less than n
proof of Dirichlet's theorem on arithmetic progressions. The Dirichlet series for φ(n) may be written in terms of the Riemann zeta function as: ∑ n =
Euler's_totient_function
Topics referred to by the same term
In mathematics, eta function may refer to: The Dirichlet eta function η(s), a Dirichlet series The Dedekind eta function η(τ), a modular form The Weierstrass
Eta_function
Theorem in measure theory
first n rationals and 0 otherwise. Then f {\displaystyle f} is the Dirichlet function on [ 0 , 1 ] {\displaystyle [0,1]} , which is not Riemann integrable
Dominated_convergence_theorem
Arithmetic function
all over the prime numbers. Arithmetic function Dirichlet L-function Dirichlet series Multiplicative function Apostol (1976), p. 30 Apostol (1976), p
Completely multiplicative function
Completely_multiplicative_function
Instantaneous rate of change (mathematics)
quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input
Derivative
(a)te^{at}}{e^{ft}-1}}} for χ a Dirichlet character with conductor f. The Kubota–Leopoldt p-adic L-function Lp(s, χ) interpolates the Dirichlet L-function with the Euler
P-adic_L-function
Special functions of several complex variables
mathematics, theta functions are special functions of several complex variables. Fundamentally, they are a family of continuous functions which encode the
Theta_function
About mathematical functions
definition that became known as Dirichlet's definition." Edwards also credits Euler with a general concept of a function and says further that The relations
History of the function concept
History_of_the_function_concept
Type of Dirichlet series associated to number field extensions
In mathematics, Artin L-functions are a type of Dirichlet series defined for finite extensions of number fields, encoding informations about linear representations
Artin_L-function
Explicit formula (L-function) Riemann–Siegel formula (particular approximate functional equation) "§25.15 Dirichlet -functions on NIST". Weisstein, Eric
Functional equation (L-function)
Functional_equation_(L-function)
Number of prime factors of a natural number
related summatory functions over so-termed factorial moments of the function ω ( n ) {\displaystyle \omega (n)} . A known Dirichlet series involving ω
Prime_omega_function
Conjecture on zeros of the zeta function
this continuation observes that the series for the zeta function and the Dirichlet eta function satisfy the relation ( 1 − 2 2 s ) ζ ( s ) = η ( s ) =
Riemann_hypothesis
Type of plane partition
Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet). Voronoi cells are also known as Thiessen polygons
Voronoi_diagram
Summatory function of the divisor-counting function
the Dirichlet divisor problem". Acta Arithmetica. 60 (4): 389–415. doi:10.4064/aa-60-4-389-415. ISSN 0065-1036. S2CID 59450869. Theorem 1 The function has
Divisor_summatory_function
Mathematical form
harmonic functions) and functional analysis, Dirichlet forms generalize the Laplacian (the mathematical operator on scalar fields). Dirichlet forms can
Dirichlet_form
Mathematical identity used to evaluate certain improper integrals
In mathematics, Dirichlet integrals play an important role in distribution theory. We can see the Dirichlet integral in terms of distributions. One of
Lobachevsky_integral_formula
Mathematical tool for summing arithmetic functions
_{k=1}^{n}f(k)} . The first step is to find a pair of functions g and h such that, using Dirichlet convolution, we have f = g ∗ h; the sum then becomes
Dirichlet_hyperbola_method
Function whose domain is the positive integers
log(n). Given an arithmetic function a(n), let Fa(s), for complex s, be the function defined by the corresponding Dirichlet series (where it converges):
Arithmetic_function
Type of mathematical function
using the Risch algorithm other nonelementary integrals, including the Dirichlet integral and elliptic integral. In elementary real-variable settings such
Elementary_function
Test for series convergence
In mathematics, Dirichlet's test is a method of testing for the convergence of a series that is especially useful for proving conditional convergence
Dirichlet's_test
Topics referred to by the same term
to: Beta function (physics), details the running of the coupling strengths Dirichlet beta function, closely related to the Riemann zeta function Gödel's
Beta function (disambiguation)
Beta_function_(disambiguation)
Mathematical relation consisting of a multi-variable function equal to zero
multivariable functions that are continuously differentiable. A common type of implicit function is an inverse function. Not all functions have a unique
Implicit_function
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
Probability distribution
Dirichlet distribution, the solution can be written in terms of the digamma ψ {\displaystyle \psi } and trigamma ψ ′ {\displaystyle \psi '} functions:
Logit-normal_distribution
Mathematical function with no sudden changes
ideas on lectures given by Peter Gustav Lejeune Dirichlet in 1854. A real function that is a function from real numbers to real numbers can be represented
Continuous_function
integer-valued function. Integer-valued functions defined on the domain of all real numbers include the floor and ceiling functions, the Dirichlet function, the
Integer-valued_function
Special function in mathematics
the Hurwitz zeta function may be expressed as a linear combination of Dirichlet L-functions and vice versa: The Hurwitz zeta function coincides with Riemann's
Hurwitz_zeta_function
Mathematical operation
theory, a Dirichlet series, or Dirichlet generating function (DGF), of a sequence is a common way of understanding and summing arithmetic functions in a meaningful
Dirichlet_series_inversion
Topics referred to by the same term
Look up lambda function in Wiktionary, the free dictionary. Lambda function may refer to: Dirichlet lambda function, λ(s) = (1 – 2−s)ζ(s) where ζ is the
Lambda_function
Function on an integer n which is log(p) if n equals p^k and zero otherwise
The von Mangoldt function plays an important role in the theory of Dirichlet series, and in particular, the Riemann zeta function. For example, one has
Von_Mangoldt_function
Arithmetic function related to the divisors of an integer
is known as Dirichlet's divisor problem. The behaviour of the sigma function is irregular. The asymptotic growth rate of the sigma function can be expressed
Divisor_function
Smooth approximation of one-hot arg max
Multinomial logistic regression Dirichlet distribution – an alternative way to sample categorical distributions Partition function Exponential tilting – a generalization
Softmax_function
Formula for the derivative of an inverse function
calculus, the inverse function rule is a formula that expresses the derivative of the inverse of a bijective and differentiable function f in terms of the
Inverse_function_rule
Mathematical function
This multivariate beta function is used in the definition of the Dirichlet distribution. Its relationship to the beta function is analogous to the relationship
Beta_function
Summability method in physics
series Minakshisundaram–Pleijel zeta function Zeta function (operator) ^ Tom M. Apostol, "Modular Functions and Dirichlet Series in Number Theory", "Springer-Verlag
Zeta_function_regularization
Type of character in number theory
generalisation of a Dirichlet character, introduced by Erich Hecke to construct a class of L-functions larger than Dirichlet L-functions, and a natural setting
Hecke_character
terms of the zeta function. The function δ {\displaystyle \delta } is multiplicative, and since it is bounded by 1, its Dirichlet series converges absolutely
Average order of an arithmetic function
Average_order_of_an_arithmetic_function
Differential operator in mathematics
in physics is that solutions to Δf = 0 in a region U are functions that make the Dirichlet energy functional stationary: E ( f ) = 1 2 ∫ U ‖ ∇ f ‖ 2
Laplace_operator
Expression of a function as an infinite sum of simpler functions
of a complex function near a singularity by considering the series expansion on an annulus centered at the singularity. A general Dirichlet series is a
Series_expansion
This is a list of some well-known periodic functions. The constant function f (x) = c, where c is independent of x, is periodic with any period, but lacks
List_of_periodic_functions
Modes of vibration in mathematics
(1) is often known as the Dirichlet Laplacian when it is considered as accepting only functions u satisfying the Dirichlet boundary condition. More generally
Dirichlet_eigenvalue
Conditions for switching order of integration in calculus
{\pi }{2}}\ln(2)\end{aligned}}} The Dirichlet series defines the Dirichlet eta function as follows: η ( s ) = ∑ n = 1 ∞ ( − 1 ) n − 1 n s
Fubini's_theorem
Matrix of second derivatives
partial derivatives of a scalar-valued function, or scalar field. It describes the local curvature of a function of many variables. The Hessian matrix
Hessian_matrix
Integral constructed using Darboux sums
\infty }L_{f,P_{n}}={\frac {1}{2}}} Darboux sums Suppose we have the Dirichlet function f : R → [ 0 , 1 ] {\displaystyle f:\mathbb {R} \to [0,1]} defined
Darboux_integral
Mathematical concept
Here y is a real parameter. The Riemann zeta function can be replaced by a Dirichlet L-function of a Dirichlet character χ. The sum over prime powers then
Explicit formulae for L-functions
Explicit_formulae_for_L-functions
DIRICHLET FUNCTION
DIRICHLET FUNCTION
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.
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
, Functionary of the Interior.
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Male
Egyptian
, an Egyptian functionary.
Male
Egyptian
, the son of the functionary Heknofre.
Male
Egyptian
, a high Egyptian functionary.
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.
Male
Celtic
, great justiciary, or functionary.
Male
Egyptian
, an Egyptian functionary.
Male
Egyptian
, a great functionary.
Biblical
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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.
DIRICHLET FUNCTION
DIRICHLET FUNCTION
Boy/Male
Tamil
Blessings of God
Boy/Male
Sikh
One, United see alt. spelling Ekam), First one
Boy/Male
Indian, Punjabi, Sikh
Of True Deeds
Girl/Female
Indian
Universe
Boy/Male
Latin American English French
meaning from France, or free one.
Boy/Male
Hindu, Indian, Marathi, Parsi, Sanskrit, Thai
Wisest Amongst the Wise
Girl/Female
English
which is the Greek form of Elijah.
Girl/Female
American, British, English, French, Irish
A Combination of Cori and Ann; From the Round Hill; Maiden; Seething Pool; Ravine
Boy/Male
Italian American Teutonic German Shakespearean Spanish
Form of Alphonse: see Alfonso.
Girl/Female
Irish
Brings joy.
DIRICHLET FUNCTION
DIRICHLET FUNCTION
DIRICHLET FUNCTION
DIRICHLET FUNCTION
DIRICHLET FUNCTION
v. t.
To assign to some function or office.
n.
The doctrine that all the functions of a living organism are due to an unknown vital principle distinct from all chemical and physical forces.
a.
Of or pertaining to the vessels of animal and vegetable bodies; as, the vascular functions.
v. i.
Alt. of Functionate
n.
Fig.: Any cavity, or hollow place, in which any function may be conceived of as operating.
a.
Belonging or relating to life, either animal or vegetable; as, vital energies; vital functions; vital actions.
pl.
of Functionary
a.
Of, pertaining to, or designating, certain secret tribunals which flourished in Germany from the end of the 12th century to the middle of the 16th, usurping many of the functions of the government which were too weak to maintain law and order, and inspiring dread in all who came within their jurisdiction.
prep.
Acting as a substitute; -- said of abnormal action which replaces a suppressed normal function; as, vicarious hemorrhage replacing menstruation.
n.
A certain function relating to a system of forces and their points of application, -- first used by Clausius in the investigation of problems in molecular physics.
a.
Pertaining to the function of an organ or part, or to the functions in general.
n.
One charged with the performance of a function or office; as, a public functionary; secular functionaries.
adv.
In a functional manner; as regards normal or appropriate activity.
a.
Pertaining to, or connected with, a function or duty; official.
a.
Having relation to growth or nutrition; partaking of simple growth and enlargement of the systems of nutrition, apart from the sensorial or distinctively animal functions; vegetal.
v. i.
To execute or perform a function; to transact one's regular or appointed business.
n.
One deputed or authorized to perform the functions of another; a substitute in office; a deputy.
a.
Destitute of function, or of an appropriate organ. Darwin.
n.
The appropriate action of any special organ or part of an animal or vegetable organism; as, the function of the heart or the limbs; the function of leaves, sap, roots, etc.; life is the sum of the functions of the various organs and parts of the body.
n.
A quantity so connected with another quantity, that if any alteration be made in the latter there will be a consequent alteration in the former. Each quantity is said to be a function of the other. Thus, the circumference of a circle is a function of the diameter. If x be a symbol to which different numerical values can be assigned, such expressions as x2, 3x, Log. x, and Sin. x, are all functions of x.