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- Anger three-term recurrence
- Antiderivative of arccos
- Antiderivative of arccosh
- Antiderivative of arcsin
- Antiderivative of arcsinh
- Antiderivative of arctan
- Antiderivative of arctanh
- Antiderivative of cosine integral
- Antiderivative of coth
- Antiderivative of hyperbolic cosecant
- Antiderivative of inverse error function
- Antiderivative of sech
- Antiderivative of sine integral
- Antiderivative of tanh
- Antiderivative of the logarithm
- Antiderivative of versine
- Apéry's constant
- Apéry's constant is irrational
- Arakawa-Kaneko zeta function
- Arccos
- Arccos as inverse cosine
- Arccosh
- Arccot
- Arccoth
- Arccsc
- Arccsch
- Arcsec
- Arcsech
- Arcsin
- Arcsin as inverse sine
- Arcsin cdf
- Arcsin pdf
- Arcsinh
- Arctan
- Arctanh
- Arithmetic functions
- Arithmetic zeta function
- Artin-Mazur zeta function
- Artin constant
- Associated Laguerre L
- Asymptotic behavior of Sievert integral
- Asymptotic formula for partition function
- B(x,y)=2^(1-x-y)integral (1+t)^(x-1)(1-t)^(y-1)+(1+t)^(y-1)(1-t)^(x-1) dt
- B(x,y)=integral (t^(x-1)+t^(y-1))(1+t)^(-x-y) dt
- B(x,y)B(x+y,z)=B(y,z)B(y+z,x)
- B(x,y)B(x+y,z)=B(z,x)B(x+z,y)
- B(x,y)B(x+y,z)B(x+y+z,u)=Gamma(x)Gamma(y)Gamma(z)Gamma(u)/Gamma(x+y+z+u)
- B(x,y+1)=(y/(x+y))B(x,y)
- B(x,y+1)=(y/x)B(x+1,y)
- Barnes G
- Barnes G at positive integer
- Barnes G at z+1 in terms of Barnes G and gamma
- Barnes zeta function
- Basic hypergeometric phi
- Basic hypergeometric series psi
- Bateman F
- Bell numbers
- Bell polynomial
- Bernardi operator
- Bernoulli-Euler Gamma function
- Bernoulli B
- Bernoulli numbers
- Bernoulli polynomial and Hurwitz zeta
- Bernstein B
- Bessel-Clifford
- Bessel J
- Bessel J in terms of Bessel-Clifford
- Bessel Y
- Bessel at -n-1/2 in terms of Bessel polynomial
- Bessel at n+1/2 in terms of Bessel polynomial
- Bessel functions footer
- Bessel polynomial
- Bessel polynomial generalized hypergeometric
- Bessel polynomial in terms of Bessel functions
- Beta
- Beta as improper integral
- Beta as product of gamma functions
- Beta in terms of gamma
- Beta in terms of power of t over power of (1+t)
- Beta in terms of sine and cosine
- Beta is symmetric
- Bickley-Naylor
- Binet's formula
- Binomial coefficient
- Binomial coefficient ((n+1) choose k) equals (n choose k) + (n choose (k-1))
- Binomial coefficient (n choose 0) equals 1
- Binomial coefficient (n choose k) equals (-1)^k ((k-n-1) choose k)
- Binomial coefficient (n choose k) equals (n choose (n-k))
- Binomial coefficient (n choose n) equals 1
- Binomial series
- Binomial theorem
- Bohr-Mollerup theorem
- Bolzano function
- Bolzano function is continuous
- Bolzano function is nowhere differentiable
- Book:Aleksandar Ivić/The Riemann Zeta-Function
- Book:Alfred George Greenhill/The applications of elliptic functions
- Book:Andrew Gray/A Treatise on Bessel Functions
- Book:Andrew Gray/A Treatise on Bessel Functions/Second Edition
- Book:Arthur Erdélyi/Higher Transcendental Functions Volume I
- Book:Arthur Erdélyi/Higher Transcendental Functions Volume II
- Book:Arthur Erdélyi/Higher Transcendental Functions Volume III
- Book:Bernard Dwork/Generalized hypergeometric functions
- Book:Charalambos Charalambides/Discrete q-Distributions
- Book:Earl David Rainville/Special Functions
- Book:Edmund Taylor Whittaker/A course of modern analysis/Third edition
- Book:Edward Charles Titchmarsh/The Zeta-Function of Riemann
- Book:Elena Deza/Figurate Numbers
- Book:F.E. Relton/Applied Bessel Functions
- Book:G.H. Hardy/The General Theory Of Dirichlet's Series
- Book:Gabor Szegő/Orthogonal Polynomials/Fourth Edition
- Book:George E. Andrews/Special Functions
- Book:George Eyre Andrews/Number Theory
- Book:Harris Hancock/Lectures on the theory of elliptic functions
- Book:Ian N. Sneddon/Special Functions of Mathematical Physics and Chemistry
- Book:Ioannis Dimitrios Avgoustis/Definite Integration using the Generalized Hypergeometric Functions
- Book:Johan Thim/Continuous Nowhere Differentiable Functions
- Book:Johann Heinrich Graf/Einleitung in die Theorie der Gammafunktion und der Euler'schen Integrale
- Book:Larry C. Andrews/Special Functions of Mathematics for Engineers
- Book:Leonard Lewin/Dilogarithms and Associated Functions
- Book:Leonard Lewin/Polylogarithms and Associated Functions/Second Edition
- Book:Leonard Lewin/Structural Properties of Polylogarithms
- Book:Michael Wilensky/Ueber Besselsche Funktionen
- Book:Milton Abramowitz/Handbook of mathematical functions
- Book:Nicholas Higham/Functions of Matrices: Theory and Computation
- Book:Norman L. Johnson/Continuous Univariate Distributions Volume 2/Second Edition
- Book:Richard Beals/Special functions, a graduate text
- Book:Richard Dedekind/Essays on the Theory of Numbers
- Book:Roelof Koekoek/Hypergeometric Orthogonal Polynomials and Their q-Analogues
- Book:Sir Thomas L. Heath/Euclid: The Thirteen Books of The Elements: Volume 2/Second Edition
- Book:T.S. Chihara/An Introduction to Orthogonal Polynomials
- Book:Thomas Ernst/A Comprehensive Treatment of q-Calculus
- Book:Victor Kac/Quantum Calculus
- Book:W.N. Bailey/Generalized Hypergeometric Series
- Book:W.W. Bell/Special Functions for Scientists and Engineers
- Book:Wilhelm Magnus/Formulas and Theorems for the Special Functions of Mathematical Physics/Third Edition
- Book:Yudell L. Luke/The Special Functions And Their Approximations, Volume I
- Boole polynomials
- Brun's constant
- Buchstab function
- Böhmer C
- Böhmer S
- C(a-(c-b)z)2F1-ac(1-z)2F1(a+1)+(c-a)(c-b)z2F1(c+1)=0
- C n^(lambda)'(x)=2lambda C (n+1)^(lambda+1)(x)
- Cahen's constant
- Catalan's constant
- Catalan's constant using Dirichlet beta
- Catalan's constant using Hurwitz zeta
- Catalan's constant using Legendre chi
- Catalan's identity
- Cauchy cdf
- Cauchy pdf
- Ceiling
- Cell
- Cellérier function
- Cellérier function is continuous
- Cellérier function is nowhere differentiable
- Chain rule for derivatives
- Chaitin's constant
- Champernowne constant
- Champernowne constant is transcendental
- Charlier polynomial
- Chebyshev T
- Chebyshev U
- Chebyshev psi function
- Chebyshev theta function
- Chi
- Clausen cosine
- Clausen sine
- Closed form for partition function with sinh
- Closed formula for physicist's Hermite polynomials
- Complex conjugate of argument of error function
- Complex number
- Constant functions are elliptic functions
- Constant multiple rule for derivatives
- Continued fraction
- Continued fraction for 1/sqrt(pi) integral from -infinity to infinity of e^(-t^2)/(z-t) dt
- Continued fraction for 2e^(z^2) integral from z to infinity e^(-t^2) dt for positive Re(z)
- Continuous
- Continuous nowhere differentiable functions footer
- Continuous q-Hermite polynomial
- Continuous uniform cdf
- Continuous uniform pdf
- Contour integral representation of reciprocal gamma
- Convergence of Hypergeometric pFq
- Copeland-Erdős constant
- Copeland-Erdős is irrational
- Copeland-Erdős is normal
- Cosecant
- Cosh
- Cosh is even
- Cosh of a sum
- Coshc
- Cosine
- Cosine integral
- Cotangent
- Cotangent zeta function
- Coth
- Coth of a sum
- Covercosine
- Coversine
- Csch
- Cyclotomic polynomials
- D/dz(z^(-nu)H (nu))=1/(sqrt(pi)2^(nu)Gamma(nu+3/2))-z^(-nu)H (nu+1)
- D/dz(z^(nu)H (nu))=z^(nu)H (nu-1)
- Darboux function
- Darboux function is continuous
- Darboux function is nowhere differentiable
- Dawson D+
- Dawson D-
- Debye function
- Dedekind eta
- Dedekind zeta function
- Denisyuk polynomials
- Depreciated trigonometric functions footer
- Derivative
- Derivative is a linear operator
- Derivative of Bessel-Clifford
- Derivative of Bessel J with respect to its order
- Derivative of Bessel Y with respect to its order
- Derivative of Gudermannian
- Derivative of Jacobi theta 1 at 0
- Derivative of Legendre chi 2
- Derivative of Li 2(-1/x)
- Derivative of Riemann zeta
- Derivative of Struve H0
- Derivative of arccos
- Derivative of arccosh
- Derivative of arccot
- Derivative of arccoth
- Derivative of arccsc
- Derivative of arcsec
- Derivative of arcsin
- Derivative of arcsinh
- Derivative of arctan
- Derivative of arctanh
- Derivative of cosecant
- Derivative of cosh
- Derivative of cosine
- Derivative of cosine integral
- Derivative of cotangent
- Derivative of coth
- Derivative of erfi
- Derivative of hyperbolic cosecant
- Derivative of inverse error function
- Derivative of prime zeta
- Derivative of secant
- Derivative of sech
- Derivative of sine
- Derivative of sine integral
- Derivative of sinh
- Derivative of tangent
- Derivative of tanh
- Derivative of the exponential function
- Derivative of the logarithm
- Derivative of versine
- Derivative of zeta at -1
- Derivatives of Hypergeometric pFq
- Devil's staircase
- Devil's staircase is continuous
- Devil's staircase is not absolutely continuous
- Dickman–de Bruijn function
- Dickson polynomial
- Difference equation of hypergeometric type
- Difference of cosh and sinh
- Differential equation for Hypergeometric pFq
- Differential equation for Jacobi P
- Digamma
- Digamma at 1
- Digamma at 1/2
- Digamma at n+1
- Digamma at n+1/2
- Digamma at z+n
- Digamma functional equation
- Dilogarithm
- Dirichlet L-function
- Dirichlet beta
- Dirichlet beta in terms of Lerch transcendent
- Dirichlet eta
- Dirichlet function
- Dirichlet function is nowhere continuous
- Dirichlet series
- Distance to integers
- Doubling identity for cosh (1)
- Doubling identity for cosh (2)
- Doubling identity for cosh (3)
- Doubling identity for sinh (1)
- Doubling identity for sinh (2)
- Doubly periodic function
- E
- E(1,1)(z)=exp(z)
- E(2,1)(-z^2)=cos(z)
- E(2,1)(z)=cosh(sqrt(z))
- E(m)=(pi/2)2F1(-1/2,1/2;1;m)
- E^(-x) less than 1-(x/2) for 0 less than x less than or equal to 1.5936
- E^(-x/(1-x)) is less than 1-x is less than e^(-x) for nonzero real x less than 1
- E^x greater than (1+x/y)^y greater than exp(xy/(x+y) for x greater than 0 and y greater than 0)
- E^x greater than 1+x^n/n! for n greater than 0 and nonzero real x greater than 0
- E^x is greater than 1+x for nonzero real x
- E^x is less than 1/(1-x) for nonzero real x less than 1
- E (0,1)(z)=1/(1-z) for abs(z) less than 1
- E is irrational
- E is limit of (1+1/n)^n
- Ei(x)=-Integral from -x to infinity of e^(-t)/t dt
- Elliptic E
- Elliptic K
- Elliptic function
- Elliptic gamma function
- Entire
- Entire exponential integral
- Epstein zeta function
- Erdős-Borwein Constant
- Erdős-Borwein Constant is irrational
- Erf of conjugate is conjugate of erf
- Erfc
- Erfi
- Error function
- Error function is odd
- Error functions footer
- Euler's formula
- Euler-Jackson q-difference operator
- Euler-Mascheroni constant
- Euler E
- Euler E generating function
- Euler E n'(x)=nE n-1(x)
- Euler numbers
- Euler phi
- Euler product
- Euler product for Riemann zeta
- Euler totient
- Euler totient is multiplicative
- Exponential
- Exponential cdf
- Exponential e in terms of basic hypergeometric phi
- Exponential integral E
- Exponential integral Ei
- Exponential integral Ei series
- Exponential of logarithm
- Exponential pdf
- Exsecant
- Exton q-exponential
- F(-n)=(-1)^(n+1)F(n)
- F(2n)=F(n)L(n)
- F(2n)=F(n+1)^2-F(n-1)^2
- F(2n+1)=F(n+1)^2+F(n)^2
- F(n+1)F(n-1)-F(n)^2=(-1)^n
- F(n+m+1)=F(n+1)F(m+1)+F(n)F(m)
- Faber F1
- Faber F1 is continuous
- Faber F1 is nowhere differentiable
- Faber F2
- Faber F2 is continuous
- Faber F2 is nowhere differentiable
- Factorial
- Faddeeva function
- Falling factorial
- Fermat numbers
- Fibonacci numbers
- Fibonacci polynomial
- Fibonacci zeta at 1 is irrational
- Fibonacci zeta function
- Fibonacci zeta in terms of a sum of binomial coefficients
- Floor
- Format notes
- Fransén–Robinson constant
- Fresnel C
- Fresnel C in terms of erf
- Fresnel C is odd
- Fresnel S
- Fresnel S in terms of erf
- Fresnel S is odd
- Full list
- Functional equation for Riemann xi
- Functional equation for Riemann zeta
- Functional equation for Riemann zeta with cosine
- Functions named after Carl Gustav Jacob Jacobi
- Functions named after Pafnuty Chebyshev
- Functions named after Peter Gustav Lejeune Dirichlet
- Fundamental pair of periods
- Gamma
- Gamma'(z)/Gamma(z)=-gamma-1/z+Sum z/(k(z+k))
- Gamma(1)=1
- Gamma(n+1)=n!
- Gamma(z)Gamma(1-z)=pi/sin(pi z)
- Gamma(z) as integral of a power of log(1/t) for Re(z) greater than 0
- Gamma(z+1)=zGamma(z)
- Gamma function written as a limit of a factorial, exponential, and a rising factorial
- Gamma function written as infinite product
- Gamma recurrence relation
- Gauss' formula for gamma function
- Gegenbauer C
- Gelfond-Schneider constant is transcendental
- Gelfond constant
- Gelfond constant is transcendental
- Gelfond–Schneider constant
- General Dirichlet series
- Generalized q-Bessel
- Generating function for Hermite (physicist) polynomials
- Generating function for Laguerre L
- Generating function for partition function
- Generating relation for Bateman F
- Genocchi numbers
- Gieseking constant
- Glaisher–Kinkelin constant
- Glyphs
- Goh-Schmutz constant
- Golden ratio
- Gompertz constant
- Goss zeta function
- Graph
- Greatest prime factor
- Gudermannian
- H (-(n+1/2))(z)=(-1)^n J (n+1/2)(z) for integer n geq 0
- H (1/2)(z)=sqrt(2/(pi z))(1-cos(z))
- H (3/2)(z)=sqrt(z/(2pi))(1+2/z^2)-sqrt(2/(pi z))(sin(z)+cos(z)/z)
- H (nu)(x) geq 0 for x gt 0 and nu geq 1/2
- Hacovercosine
- Hacoversine
- Hadamard gamma
- Hahn-Exton q-Bessel
- Hahn polynomial
- Halving identity for cosh
- Halving identity for sinh
- Halving identity for tangent (1)
- Halving identity for tangent (2)
- Halving identity for tangent (3)
- Hankel H (1)
- Hankel H (1) in terms of csc and Bessel J
- Hankel H (2)
- Hankel H (2) in terms of csc and Bessel J
- Hankel functions footer
- Harmonic number
- Havercosine
- Haversine
- Heaviside step function
- Hermite (physicist)
- Hermite (physicist) polynomial at negative argument
- Hermite (probabilist)
- Humbert polynomials
- Hurwitz zeta
- Hurwitz zeta absolute convergence
- Hyperbolic trigonometric functions footer
- Hyperfactorial
- Hyperfactorial in terms of K-function
- Hypergeometric 0F0
- Hypergeometric 0F1
- Hypergeometric 0F3
- Hypergeometric 1F0
- Hypergeometric 1F1
- Hypergeometric 1F2
- Hypergeometric 2F0
- Hypergeometric 2F1
- Hypergeometric 2F3
- Hypergeometric 3F2
- Hypergeometric 4F1
- Hypergeometric functions footer
- Hypergeometric pFq
- Identity
- Identity written as a sum of Möbius functions
- Ihara zeta function
- Imaginary number
- Incomplete Elliptic E
- Incomplete Elliptic K
- Incomplete beta function
- Integer
- Integers
- Integral (t-b)^(x-1)(a-t)^(y-1)dt=(a-b)^(x+y-1)B(x,y)
- Integral from a to a
- Integral of (1+bt^z)^(-y)t^x dt = (1/z)*b^(-(x+1)/z) B((x+1)/z,y-(x+1)/z)
- Integral of (1+t)^(2x-1)(1-t)^(2y-1)(1+t^2)^(-x-y)dt=2^(x+y-2)B(x,y)
- Integral of (t-b)^(x-1)(a-t)^(y-1)/(c-t)^(x+y) dt = (a-b)^(x+y-1)/((c-a)^x (c-b)^y) B(x,y)
- Integral of (t-b)^(x-1)(a-t)^(y-1)/(t-x)^(x+y) dt=(a-b)^(x+y-1)/((a-c)^x(b-c)^y) B(x,y)
- Integral of (z^n)log(z)dz=(z^(n+1)/(n+1))log(z)-z^(n+1)/(n+1)^2 for integer n neq -1
- Integral of Bessel J for Re(nu) greater than -1
- Integral of Bessel J for nu=1
- Integral of Bessel J for nu=2n
- Integral of Bessel J for nu=2n+1
- Integral of Bessel J for nu=n+1
- Integral of inverse erf from 0 to 1
- Integral of log of inverse erf from 0 to 1
- Integral of monomial times Bessel J
- Integral of t^(x-1)(1-t^z)^(y-1) dt=(1/z)B(x/z,y)
- Integral representation of Airy Ai
- Integral representation of Struve function
- Integral representation of Struve function (2)
- Integral representation of Struve function (3)
- Integral representation of polygamma 2
- Integral representation of polygamma for Re(z) greater than 0
- Integral t^(x-1)(1+bt)^(-x-y) dt = b^(-x) B(x,y)
- Integral t^(x-1)(1-t)^(y-1)(1+bt)^(-x-y)dt = (1+b)^(-x)B(x,y)
- Integration by parts
- Inverse Gudermannian
- Inverse error function
- Inverse hyperbolic trigonometric functions footer
- Inverse trigonometric functions footer
- Irrational
- Jackson q-Bessel (1)
- Jackson q-Bessel (2)
- Jacobi P
- Jacobi cd
