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Topics referred to by the same term
Explicit formula can refer to: Closed-form expression, a mathematical expression in terms of a finite number of well-known functions Analytical expression
Explicit_formula
Mathematical formula involving a given set of operations
In mathematics, a closed form expression or formula is one that is formed with constants, variables, and a set of functions considered as basic and connected
Closed-form_expression
Mathematical concept
Number of Primes Less Than a Given Magnitude" Riemann sketched an explicit formula (it was not fully proven until 1895 by von Mangoldt, see below) for
Explicit formulae for L-functions
Explicit_formulae_for_L-functions
Approaches for approximating solutions to differential equations
each k = 0 , 1 , … , n . {\displaystyle k=0,1,\dots ,n.} This is an explicit formula for y k + 1 {\displaystyle y_{k+1}} . Backward Euler method With the
Explicit_and_implicit_methods
Mathematical model of financial markets
enables pricing using numerical methods when an explicit formula is not possible. The Black–Scholes formula has only one parameter that cannot be directly
Black–Scholes_model
Formula in Lie theory
(1906). The first actual explicit formula, with all numerical coefficients, is due to Eugene Dynkin (1947). The history of the formula is described in detail
Baker–Campbell–Hausdorff formula
Baker–Campbell–Hausdorff_formula
Solitons in Euclidean spacetime
_{a}=-\infty } and τ b = ∞ {\displaystyle \tau _{b}=\infty } . The explicit formula for the instanton solution is given by x ( τ ) = tanh ( 1 2 ( τ −
Instanton
Polynomial sequence
_{0}^{x}B_{m-1}(t)\,dt-m\int _{0}^{1}\int _{0}^{t}B_{m-1}(s)\,dsdt.} An explicit formula for the Bernoulli polynomials is given by B n ( x ) = ∑ k = 0 n [ 1
Bernoulli_polynomials
Numbers parameterizing ways to partition a set
{n}{k}}\end{aligned}}} The Stirling numbers of the second kind are given by the explicit formula: { n k } = 1 k ! ∑ j = 0 k ( − 1 ) k − j ( k j ) j n = ∑ j = 0 k (
Stirling numbers of the second kind
Stirling_numbers_of_the_second_kind
Formula whose values are the prime numbers
In number theory, a formula for primes is a formula that outputs prime numbers. Such formulas for calculating primes do exist; however, they are computationally
Formula_for_primes
Linear operator acting on modular forms
n)}d^{k-1}a\left({\frac {mn}{d^{2}}}\right).} One can see from this explicit formula that Hecke operators with different indices commute and that if a (
Hecke_operator
Mathematical problem
long as the set of coin denominations is setwise coprime. There is an explicit formula for the Frobenius number when there are only two different coin denominations
Coin_problem
Large number coined by Ronald Graham
a power of three. However, Graham's number can be explicitly given by computable recursive formulas using Knuth's up-arrow notation or equivalent, as
Graham's_number
Mathematical operation in calculus
derivative of a function that is defined by an equation rather than by an explicit formula. If an equation such as F ( x , y ) = 0 {\displaystyle F(x,y)=0} defines
Implicit_differentiation
Integer that is both a perfect square and a triangular number
OEIS: A001108 respectively. In 1778 Leonhard Euler determined the explicit formula N k = ( ( 3 + 2 2 ) k − ( 3 − 2 2 ) k 4 2 ) 2 . {\displaystyle \displaystyle
Square_triangular_number
Algorithm for computing polynomial coefficients
^{(k)}y_{j}.} When the data points are equispaced we can also derive an explicit formula for [ y j , … , y j + k ] {\displaystyle [y_{j},\ldots ,y_{j+k}]}
Divided_differences
Type of permutation
MathWorld. Ross Tang, "An Explicit Formula for the Euler zigzag numbers (Up/down numbers) from power series" A simple explicit formula for An. "A Survey of
Alternating_permutation
Count of permutations by cycles
the symmetric formulae for Stirling numbers in conjunction with the explicit formula for Stirling numbers of the second kind. [ n k ] = ∑ j = n 2 n − k
Stirling numbers of the first kind
Stirling_numbers_of_the_first_kind
Formula for systems of linear equations
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever
Cramer's_rule
Mathematical model in nuclear physics
the reverse sense (i+1 to i is forbidden). Bateman found a general explicit formula for the amounts by taking the Laplace transform of the variables. N
Bateman_equation
Integers occurring in the coefficients of the Taylor series of 1/cosh t
_{\ell =0}^{2k}(-1)^{\ell }{\binom {2k}{\ell }}(k-\ell )^{2n}.} An explicit formula for Euler numbers is E 2 n = i ∑ k = 1 2 n + 1 ∑ ℓ = 0 k ( k ℓ ) (
Euler_numbers
Mathematical theorem
Riemann surface. In this case the Selberg trace formula is formally similar to the explicit formulas relating the zeros of the Riemann zeta function to
Selberg_trace_formula
Function representing the number of primes less than or equal to a given number
S2CID 117968965. Hutama, Daniel (2017). "Implementation of Riemann's Explicit Formula for Rational and Gaussian Primes in Sage" (PDF). Institut des sciences
Prime-counting_function
Bet sizing formula for long-term growth
{\displaystyle S^{o}} of outcomes on which it is reasonable to bet and it gives explicit formula for finding the optimal fractions f k o {\displaystyle f_{k}^{o}} of
Kelly_criterion
Approximation for factorials
{571}{2488320n^{4}}}+{\frac {163879}{209018880n^{5}}}-\cdots \right).} An explicit formula for the coefficients in this series was given by G. Nemes. Further
Stirling's_approximation
Function studied by Ramanujan
-1{\pmod {23}}{\text{ otherwise}}.} In 1972, Ian G. Macdonald proved an explicit formula for the Ramanujan tau function τ ( n ) = 1 1 ! 2 ! 3 ! 4 ! ∑ x 1 +
Ramanujan_tau_function
Polynomial equation of degree 3
ISBN 978-0-521-88068-8 Rechtschaffen, Edgar (July 2008), "Real roots of cubics: Explicit formula for quasi-solutions", Mathematical Gazette, 92, Mathematical Association:
Cubic_equation
Conjecture on zeros of the zeta function
geodesics rather than primes. The Selberg trace formula is the analogue for these functions of the explicit formulas in prime number theory. Selberg proved that
Riemann_hypothesis
Polynomial sequence
For an arbitrary n, these polynomials may be computed explicitly via the following summation formula ψ n ( x ) = 1 ( n − 1 ) ! ∑ l = 0 n − 1 s ( n − 1 ,
Bernoulli polynomials of the second kind
Bernoulli_polynomials_of_the_second_kind
Even integers as sums of two primes
Pintz, Janos (2018), A new explicit formula in the additive theory of primes with applications I. The explicit formula for the Goldbach and Generalized
Goldbach's_conjecture
In mathematics, the Kontsevich quantization formula describes how to construct a generalized ★-product operator algebra from a given arbitrary finite-dimensional
Kontsevich quantization formula
Kontsevich_quantization_formula
Characterization of how many integers are prime
and nontrivial) of the zeta function. This striking formula is one of the so-called explicit formulas of number theory, and is already suggestive of the
Prime_number_theorem
System of complete and orthogonal polynomials
.} This formula enables derivation of a large number of properties of the P n {\displaystyle P_{n}} 's. Among these are explicit representations
Legendre_polynomials
Unique strong solution of a stochastic differential equation
martingales and in the calculation of characteristic functions. Yor's formula: for any two semimartingales U {\displaystyle U} and V {\displaystyle V}
Doléans-Dade_exponential
Physics problem related to laws of motion and gravity
gravitating bodies are not integrable and cannot be solved to give explicit formulas for the positions of the bodies as a function of time. For most initial
Three-body_problem
Mathematical theorem related to real and functional analysis
Gruyer, Erwan; Mudarra, Carlos (2021). "Kirszbraun's Theorem via an Explicit Formula". Canadian Mathematical Bulletin. 64 (1): 142–153. arXiv:1810.10288
Kirszbraun_theorem
Expression for sums of powers
{1}{12}}S_{4}+{\frac {7}{12}}S_{6}+{\frac {1}{3}}S_{8}} – are known, no explicit formula for S m N {\displaystyle S_{m}^{\;N}} for positive integers m {\displaystyle
Faulhaber's_formula
Jewish bankruptcy guidance
decreasing down to half this sum. Elishakoff and Dancygier present an explicit formula for the CG rule for n claimants. CG satisfies independence of irrelevant
Contested_garment_rule
Polynomial sequence
) t k . {\displaystyle A_{n}(t)=\sum _{k=0}^{n}A(n,k)\,t^{k}.} An explicit formula for A ( n , k ) {\textstyle A(n,k)} is A ( n , k ) = ∑ i = 0 k ( −
Eulerian_number
Approximation of a function by a polynomial
neighborhood of the center of expansion, but for this purpose there are explicit formulas for the remainder term (given below) which are valid under some additional
Taylor's_theorem
Infinite product converging to 2/π
mathematical formula, Viète formulated the first instance of an infinite product known in mathematics, and the first example of an explicit formula for the
Viète's_formula
Partial differential equation
nonlinearity into a linear heat equation. In particular, it provides an explicit formula for fairly general solutions of the PDE in terms of the initial datum
Cole–Hopf_transformation
Use of functions that call themselves
all recursive functions have an explicit solution, the Tower of Hanoi sequence can be reduced to an explicit formula. The binary search algorithm is a
Recursion_(computer_science)
Representation method in chemistry
skeletal formula, line-angle formula, bond-line formula or shorthand formula of an organic compound is a type of minimalist structural formula representing
Skeletal_formula
Rational number sequence
+1/2) which is an explicit formula for Bernoulli numbers and can be used to prove Von-Staudt Clausen theorem. The two main formulas relating the unsigned
Bernoulli_number
Mathematical constant related to the cosine function
\cos \left({\frac {\pi }{180}}x\right)=x} . Kaplan does not give an explicit formula for the terms of the series, which follows trivially from the Lagrange
Dottie_number
Device in the representation theory of Lie groups
In mathematics, the unitarian trick (or unitary trick) is a device in the representation theory of Lie groups, introduced by Adolf Hurwitz (1897) for the
Unitarian_trick
Most widely known generalized inverse of a matrix
and A ∗ A {\displaystyle A^{*}A} is invertible. In this case, an explicit formula is: A + = ( A ∗ A ) − 1 A ∗ . {\displaystyle A^{+}=\left(A^{*}A\right)^{-1}A^{*}
Moore–Penrose_inverse
Mathematical relation consisting of a multi-variable function equal to zero
derivative of a function that is defined by an equation rather than by an explicit formula. If an equation such as F ( x , y ) = 0 {\displaystyle F(x,y)=0} defines
Implicit_function
Method for estimating the unknown parameters in a linear regression model
β ^ {\displaystyle b={\hat {\beta }}} , which can be given by the explicit formula[proof] β ^ = argmin b ∈ R p S ( b ) = ( X T X ) − 1 X T y . {\displaystyle
Ordinary_least_squares
Mathematical function
}}\end{cases}}} From the Taylor series for the logarithm, the last term in the explicit formula can be understood as a summation of xω/ω over the trivial zeros of
Chebyshev_function
Function on an integer n which is log(p) if n equals p^k and zero otherwise
{\displaystyle x/\log x} . Von Mangoldt provided a rigorous proof of an explicit formula for ψ ( x ) {\displaystyle \psi (x)} involving a sum over the non-trivial
Von_Mangoldt_function
Study of the topology of a complex manifold
_{i}} where δi is the vanishing cycle of xi. This formula appears implicitly for k = 2 (without the explicit coefficients of the vanishing cycles δi) in Picard
Picard–Lefschetz_theory
Riemannian metric on the space of mixed states of a quantum system
great circles on the hypersphere, and we also obtain the Wootters distance formula. If both density operators are pure states, ψ {\displaystyle \psi }
Bures_metric
Matrix of geometric progressions
Vandermonde matrix is invertible if and only if the xi are distinct. An explicit formula for the inverse is known (see below). If the columns of the Vandermonde
Vandermonde_matrix
Probability distribution of the sum of random variables
properties of the resulting distribution, such as moments, even if an explicit formula for the distribution itself cannot be derived. One of the straightforward
Convolution of probability distributions
Convolution_of_probability_distributions
Measure of curvature in differential geometry
geometry of the metric near that point. It is defined by a complicated explicit formula in terms of partial derivatives of the metric components, although
Scalar_curvature
Type of matrix factorization
When an LDU factorization exists and is unique, there is a closed (explicit) formula for the elements of L, D, and U in terms of ratios of determinants
LU_decomposition
Generalization of mass, length, area and volume
{\displaystyle \mu _{0-\infty }} defined in the above theorem. Here is an explicit formula for μ 0 − ∞ {\displaystyle \mu _{0-\infty }} : μ 0 − ∞ = ( sup { μ
Measure_(mathematics)
Supersonic flow past a slender body
developed the theory in 1932. The theory, in particular, provides an explicit formula for the wave drag, which converts the kinetic energy of the moving
Kármán–Moore_theory
Polynomials in combinatorial mathematics
also occur in many applications, such as in Faà di Bruno's formula and an explicit formula for Lagrange inversion. The partial or incomplete exponential
Bell_polynomials
Polynomial sequence
to obtain more general analytic functions for complex-valued λ. An explicit formula of Hermite polynomials in terms of contour integrals (Courant & Hilbert
Hermite_polynomials
Nonlinear relationship between stress and strain
{\sigma }{\sigma _{y}}}\right)^{n}} The Ramberg-Osgood model provides an explicit formula for obtaining strain ε {\displaystyle \varepsilon } from stress σ {\displaystyle
Ramberg–Osgood_relationship
representability of this function by explicit formulas. The strongest known results on the unexpressibility of functions by explicit formulas have been obtained in this
Topological_Galois_theory
French mathematician (1906-1998)
List Bergman–Weil formula Borel–Weil theorem Chern–Weil homomorphism Chern–Weil theory De Rham–Weil theorem Weil's explicit formula Hasse–Weil Bound Hasse–Weil
André_Weil
Distance from a point to the boundary of a set
that f is twice continuously differentiable on it, then there is an explicit formula involving the Weingarten map Wx for the Jacobian of changing variables
Signed_distance_function
square-root matrices. In many cases, such a matrix R can be obtained by an explicit formula. Square roots that are not the all-zeros matrix come in pairs: if R
Square root of a 2 by 2 matrix
Square_root_of_a_2_by_2_matrix
Gives conditions for the solvability of quadratic equations modulo prime numbers
{\displaystyle p\equiv 3{\pmod {4}}} using Euler's criterion one can give an explicit formula for the "square roots" modulo p {\displaystyle p} of a quadratic residue
Quadratic_reciprocity
Example of a phase-space star product in mathematics
order n, characterized by the following properties (see below for an explicit formula): f ⋆ g = f g + O ( ℏ ) , {\displaystyle f\star g=fg+{\mathcal {O}}(\hbar
Moyal_product
Amplifier that converts current to voltage
iterative method often required to optimize the value. There is no explicit formula for calculating the capacitor value that works for all cases. A compensation
Transimpedance_amplifier
Four basic unsolved problems about prime numbers
353–370. doi:10.4064/aa-27-1-353-370. Pintz, Janos (2018). "A new explicit formula in the additive theory of primes with applications II. The exceptional
Landau's_problems
Type of differential equation
solves the equation. However, it is often impossible to write down explicit formulas for solutions of partial differential equations. Hence there is a
Partial_differential_equation
In mathematics, an explicit reciprocity law is a formula for the Hilbert symbol of a local field. The name "explicit reciprocity law" refers to the fact
Explicit_reciprocity_law
Mathematical conjecture about the Riemann zeta function
statements. He gives a geometric interpretation of the explicit formula of number theory as a trace formula on noncommutative geometry of Adele classes. A possible
Hilbert–Pólya_conjecture
{\displaystyle f(z)=1/(z^{k}-1)^{2},g(z)=z^{k-1}\,\!} . This produces the explicit formula X ( z ) = 1 2 ℜ { ( − 1 k z ( z k − 1 ) ) [ ( k − 1 ) ( z k − 1 ) 2
K-noid
Type of functional equation (mathematics)
solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation
Differential_equation
Principle in mathematical optimization
\lambda } . But for some classes of functions, it is possible to get an explicit formula for g ( λ ) {\displaystyle g(\lambda )} . Solving the primal and dual
Duality_(optimization)
Special mathematical function defined as sin(x)/x
function can not be obtained by a simple tensor product. However, the explicit formula for the sinc function for the hexagonal, body-centered cubic, face-centered
Sinc_function
Fundamental solution to the heat equation, given boundary values
y)\phi (y)\,dy=\phi (x).} On a more general domain Ω in Rd, such an explicit formula is not generally possible. The next simplest cases of a disc or square
Heat_kernel
Operation in mathematical calculus
mathematics, physics, and engineering involve integration where an explicit formula for the integral is desired. Extensive tables of integrals have been
Integral
How many ways a positive integer can be represented as the sum of four squares
not divisible by 4. In particular, for a prime number p we have the explicit formula r4(p) = 8(p + 1). Some values of r4(n) occur infinitely often as r4(n)
Jacobi's_four-square_theorem
Integral expressing the amount of overlap of one function as it is shifted over another
satisfy S − 1 ∗ S = δ {\displaystyle S^{-1}*S=\delta } from which an explicit formula for S−1 may be obtained. The set of invertible distributions forms
Convolution
Compact notation for chemical compounds
A chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule
Chemical_formula
Theorem: (cos x + i sin x)^n = cos nx + i sin nx
In mathematics, de Moivre's formula (also known as de Moivre's theorem and de Moivre's identity) states that for any real number x and integer n, ( cos
De_Moivre's_formula
Coefficients in angular momentum eigenstates of quantum systems
coefficients can be found. There also exist complicated explicit formulas for their direct calculation. The formulas below use Dirac's bra–ket notation and the Condon–Shortley
Clebsch–Gordan_coefficients
French mathematician (born 1948)
generator of the geodesic flow. One striking application is Bismut's explicit formulas for all orbital integrals at semi-simple elements of any reductive
Jean-Michel_Bismut
Mathematics concept
x ∈ { 0 , 1 } Z {\displaystyle x\in \{0,1\}^{\mathbb {Z} }} by an explicit formula. Let [ F n ( x ) ] j {\displaystyle [F^{n}(x)]_{j}} represent the state
Elementary_cellular_automaton
Special function defined by an integral
{\displaystyle N=5} in pink). Using integration by parts, we can obtain an explicit formula E i ( z ) = e z z ( ∑ k = 0 n k ! z k + e n ( z ) ) , e n ( z ) ≡ (
Exponential_integral
Way of calculating the day of the week of a given date
(8 mod 7) = 7 − 1 = 6 Doomsday for 2005 = 6 + Tuesday = Monday The explicit formula for the odd+11 method is: 7 − [ y + 11 ( y mod 2 ) 2 + 11 ( y + 11
Doomsday_rule
Estimate of velocity in open channel flows
The Manning formula or Manning's equation is an empirical formula estimating the average velocity of a liquid in an open channel flow (flowing in a conduit
Manning_formula
Graphic representation of a molecular structure
bonding within the molecule is also shown, either explicitly or implicitly. Unlike other chemical formula types, which have a limited number of symbols and
Structural_formula
Large number used in number theory
given how far one has to go to find the first example. Riemann gave an explicit formula for π ( x ) {\displaystyle \pi (x)} , whose leading terms are (ignoring
Skewes's_number
Formula for the Legendre polynomials
expressing t in terms of u in the general formula just given for G ( x , u ) {\displaystyle G(x,u)} , explicit formulas for G ( x , u ) {\displaystyle G(x,u)}
Rodrigues'_formula
In the mathematical field of potential theory, Boggio's formula is an explicit formula for the Green's function for the polyharmonic Dirichlet problem
Boggio's_formula
Form of interpolation
There is always a unique such polynomial, commonly given by two explicit formulas, the Lagrange polynomials and Newton polynomials. The original use
Polynomial_interpolation
Riemann's differential equation Riemann's existence theorem Riemann's explicit formula Riemann's minimal surface Riemann's theorem on removable singularities
List of things named after Bernhard Riemann
List_of_things_named_after_Bernhard_Riemann
Equations for calculations of the Darcy friction factor
1943-7900.0001540. ISSN 0733-9429. Haaland, SE (1983). "Simple and Explicit Formulas for the Friction Factor in Turbulent Flow". Journal of Fluids Engineering
Darcy friction factor formulae
Darcy_friction_factor_formulae
Algorithm for division of polynomials
be factored out to obtain a quartic (fourth degree) quotient; the explicit formula for the roots of a quartic polynomial can then be used to find the
Polynomial_long_division
Mathematical functions
{1}{2}}\cdot {\frac {1\cdot 3\cdots (2k-1)}{2\cdot 4\cdots (2k)}}} . Explicit formulas are g n ( x ) = ∑ k = 1 n 2 k − 1 ( n − 1 n − k ) ( x k ) = ∑ k =
Mittag-Leffler_polynomials
German mathematician (1826–1866)
non-trivial zeros on the line with real portion 1/2, he gave an exact, "explicit formula" for π ( x ) {\displaystyle \pi (x)} . Riemann knew of Pafnuty Chebyshev's
Bernhard_Riemann
EXPLICIT FORMULA
EXPLICIT FORMULA
Surname or Lastname
English
English : from Old English dǣd ‘deed’, ‘exploit’; probably a nickname commemorating some exploit perpetrated by the bearer or for someone noted for his derring-do.
Surname or Lastname
English
English : from Old English Englisc. The word had originally distinguished Angles (see Engel) from Saxons and other Germanic peoples in the British Isles, but by the time surnames were being acquired it no longer had this meaning. Its frequency as an English surname is somewhat surprising. It may have been commonly used in the early Middle Ages as a distinguishing epithet for an Anglo-Saxon in areas where the culture was not predominantly English--for example the Danelaw area, Scotland, and parts of Wales--or as a distinguishing name after 1066 for a non-Norman in the regions of most intensive Norman settlement. However, explicit evidence for these assumptions is lacking, and at the present day the surname is fairly evenly distributed throughout the country.Irish : see Golightly.
Surname or Lastname
Irish
Irish : reduced form of McDade, ‘son of David’.German : from the Frisian personal name Dode, which Bahlow explains as a form derived from baby talk.English (Norfolk) : from Old English dǣd ‘deed’, ‘exploit’, probably applied as a nickname commemorating some exploit perpetrated by the bearer or for someone noted for his derring-do. Compare Deeds.
Boy/Male
Hindu, Indian
King of Enchanting Formulas
EXPLICIT FORMULA
EXPLICIT FORMULA
Male
Arthurian
, a son of Bran; (beloved).
Girl/Female
Indian
Favor, Grace
Boy/Male
Hindu
Extremely mighty
Surname or Lastname
English
English : unexplained; see Mustain.
Boy/Male
Indian, Malayalam, Traditional
Stronger
Girl/Female
Hindu
Girl/Female
Indian
As beautiful as the Moon
Girl/Female
Muslim
Quail. Solace. Consolation.
Boy/Male
American, Australian, Christian, Dutch, Hebrew
God Gives Strength
Boy/Male
Indian, Sanskrit
Free from Disease
EXPLICIT FORMULA
EXPLICIT FORMULA
EXPLICIT FORMULA
EXPLICIT FORMULA
EXPLICIT FORMULA
a.
A word formerly used (as finis is now) at the conclusion of a book to indicate the end.
adv.
Avowedly; explicitly.
a.
Resting on another; trusting in the word or authority of another, without doubt or reserve; unquestioning; complete; as, implicit confidence; implicit obedience.
imp. & p. p.
of Elicit
a.
Tacitly comprised; fairly to be understood, though not expressed in words; implied; as, an implicit contract or agreement.
v. t.
Illustrious act; achievement; exploit.
v. t.
To elicit.
v. t.
To draw out or entice forth; to bring to light; to bring out against the will; to deduce by reason or argument; as, to elicit truth by discussion.
n.
State or quality of being implicit.
n.
An explicit declaration.
p. pr. & vb. n.
of Elicit
a.
Having no disguised meaning or reservation; unreserved; outspoken; -- applied to persons; as, he was earnest and explicit in his statement.
imp. & p. p.
of Explicate
n.
To utilize; to make available; to get the value or usefulness out of; as, to exploit a mine or agricultural lands; to exploit public opinion.
n.
The quality of being explicit; clearness; directness.
a.
Not explicit; not clearly stated; indefinite; vague.
a.
Not implied merely, or conveyed by implication; distinctly stated; plain in language; open to the understanding; clear; not obscure or ambiguous; express; unequivocal; as, an explicit declaration.
p. pr. & vb. n.
of Explicate
adv.
In an explicit manner; clearly; plainly; without disguise or reservation of meaning; not by inference or implication; as, he explicitly avows his intention.
n.
Exploit.