All pages
- (b-a)2F1+a2F1(a+1)-b2F1(b+1)=0
- (c-2a-(b-a)z)2F1+a(1-z)2F1(a+1)-(c-a)2F1(a-1)=0
- (c-a-1)2F1+a2F1(a+1)-(c-1)2F1(c-1)=0
- (c-a-b)2F1+a(1-z)2F1(a+1)-(c-b)2F1(b-1)=0
- (c-a-b)2F1-(c-a)2F1(a-1)+b(1-z)2F1(b+1)=0
- (n+1)L (n+1)(x) = (2n+1-x)L n(x)-nL (n-1)(x)
- (n+2)C (n+2)^(lambda)(x)=2(lambda+n+1)xC (n+1)^(lambda)(x)-(2lambda+n)C n^(lambda)(x)
- (n+2lambda)C n^(lambda)(x)=2lambda(C n^(lambda+1)(x)-xC (n-1)^(lambda+1)(x))
- (z/(1-q))2Phi1(q,q;q^2;z)=Sum z^k/(1-q^k)
- *-c functions footer
- *-integral functions footer
- -log(1-x) less than x/(1-x)
- 0!=1
- 0F0(;;z)=exp(z)
- 0F1(;r;z)0F1(;r;-z)=0F3(r,r/2,r/2+1/2;-z^2/4)
- 0F1(;r;z)0F1(;s;z)=2F1(r/2+s/2, r/2+s/2-1/2;r,s,r+s-1;4z)
- 1+x greater than exp(x/(1+x)) for nonzero real x greater than -1
- 1/B(n,m)=m((n+m-1) choose (n-1))
- 1/B(n,m)=n((n+m-1) choose (m-1))
- 1/q-number as a q-number
- 1F1(a;2a;z)1F1(b;2b;-z)=2F3(a/2+b/2,a/2+b/2+1/2;a+1/2,b+1/2,a+b;z^2/4)
- 1F1(a;r;z)1F1(a;r;-z)=2F3(a,r-a;r,r/2,r/2+1/2;z^2/4)
- 1Phi0(a;;z)1Phi0(b;;az)=1Phi0(ab;;z)
- 1Phi0(a;;z) as infinite product
- 2F0(a,b;;z)2F0(a,b;;-z)=4F1(a,b,a/2+b/2,a/2+b/2+1/2;a+b;4z^2)
- 2F1(1,1;2;z)=-log(1-z)/z
- 2F1(1/2,1/2;3/2;z^2)=arcsin(z)/z
- 2F1(1/2,1;3/2;-z^2)=arctan(z)/z
- 2F1(1/2,1;3/2;z^2)=log((1+z)/(1-z))/(2z)
- 2F1(a,b;a+b+1/2;z)^2=3F2(2a,a+b,2b;a+b+1/2,2a+2b;z)
- 2Phi1(q,-1;-q;z)=1+2Sum z^k/(1+q^k)
- 2cos(mt)cos(nt)=cos((m+n)t)+cos((m-n)t)
- Abel p
- Abs(e^z-1) less than or equal to e^(abs(z))-1 less than or equal to abs(z)e^(abs(z))
- Abs(log(1+z)) less than or equal to -log(1-abs(z))
- Abs(log(1-x)) less than 3x/2
- Abs(z)/4 less than abs(e^z-1) less than (7abs(z))/4 for 0 less than abs(z) less than 1
- Absolute convergence of secant zeta function
- Airy Ai
- Airy Bi
- Airy functions footer
- Airy zeta function
- Airy zeta function at 2
- Alexander operator
- Algebraic
- Algebraic number
- Alternating sum over bottom of binomial coefficient with top fixed equals 0
- Anger derivative recurrence
- Anger function
- Anger of integer order is Bessel J
- 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
