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View (previous 250 | next 250) (20 | 50 | 100 | 250 | 500)- B(x,y)=integral (t^(x-1)+t^(y-1))(1+t)^(-x-y) dt (transclusion) (← links)
- B(x,y+1)=(y/x)B(x+1,y) (transclusion) (← links)
- B(x,y+1)=(y/(x+y))B(x,y) (transclusion) (← links)
- B(x,y)B(x+y,z)=B(y,z)B(y+z,x) (transclusion) (← links)
- B(x,y)B(x+y,z)=B(z,x)B(x+z,y) (transclusion) (← links)
- 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) (transclusion) (← links)
- 1/B(n,m)=m((n+m-1) choose (n-1)) (transclusion) (← links)
- 1/B(n,m)=n((n+m-1) choose (m-1)) (transclusion) (← links)
- 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 (transclusion) (← links)
- Integral t^(x-1)(1-t)^(y-1)(1+bt)^(-x-y)dt = (1+b)^(-x)B(x,y) (transclusion) (← links)
- Integral t^(x-1)(1+bt)^(-x-y) dt = b^(-x) B(x,y) (transclusion) (← links)
- Integral (t-b)^(x-1)(a-t)^(y-1)dt=(a-b)^(x+y-1)B(x,y) (transclusion) (← links)
- 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) (transclusion) (← links)
- 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) (transclusion) (← links)
- Integral of (1+bt^z)^(-y)t^x dt = (1/z)*b^(-(x+1)/z) B((x+1)/z,y-(x+1)/z) (transclusion) (← links)
- Integral of t^(x-1)(1-t^z)^(y-1) dt=(1/z)B(x/z,y) (transclusion) (← links)
- Integral of (1+t)^(2x-1)(1-t)^(2y-1)(1+t^2)^(-x-y)dt=2^(x+y-2)B(x,y) (transclusion) (← links)
- Li2(z)=zPhi(z,2,1) (transclusion) (← links)
- Logarithm base a (transclusion) (← links)
- Log base a in terms of logarithm base b (transclusion) (← links)
- Log a(b)=1/log b(a) (transclusion) (← links)
- Log e(z)=log(z) (transclusion) (← links)
- Log 10(z)=log(z)/log(10) (transclusion) (← links)
- Log 10(z)=log 10(e)log(z) (transclusion) (← links)
- Log(z)=log(10)log 10(z) (transclusion) (← links)
- Limit of log(x)/x^a=0 (transclusion) (← links)
- Limit of x^a log(x)=0 (transclusion) (← links)
- X/(1+x) less than log(1+x) (transclusion) (← links)
- Log(1+x) less than x (transclusion) (← links)
- X less than -log(1-x) (transclusion) (← links)
- -log(1-x) less than x/(1-x) (transclusion) (← links)
- Abs(log(1-x)) less than 3x/2 (transclusion) (← links)
- Log(x) less than or equal to x-1 (transclusion) (← links)
- Log(x) less than or equal to n(x^(1/n)-1) (transclusion) (← links)
- Abs(log(1+z)) less than or equal to -log(1-abs(z)) (transclusion) (← links)
- Log(1+z) as continued fraction (transclusion) (← links)
- Log((1+z)/(1-z)) as continued fraction (transclusion) (← links)
- Li 2(z)=-Li 2(1/z)-(1/2)(log z)^2 + i pi log(z) + pi^2/3 (transclusion) (← links)
- Two-dimensional Laplace transform (transclusion) (← links)
- Unit step function (transclusion) (← links)
- Pythagorean identity for tanh and sech (transclusion) (← links)
- Pythagorean identity for coth and csch (transclusion) (← links)
- Sum of cosh and sinh (transclusion) (← links)
- Difference of cosh and sinh (transclusion) (← links)
- Sinh is odd (transclusion) (← links)
- Cosh is even (transclusion) (← links)
- Tanh is odd (transclusion) (← links)
- Sinh of a sum (transclusion) (← links)
- Cosh of a sum (transclusion) (← links)
- Tanh of a sum (transclusion) (← links)
- Coth of a sum (transclusion) (← links)
- Halving identity for sinh (transclusion) (← links)
- Halving identity for cosh (transclusion) (← links)
- Halving identity for tangent (1) (transclusion) (← links)
- Halving identity for tangent (2) (transclusion) (← links)
- Halving identity for tangent (3) (transclusion) (← links)
- Doubling identity for sinh (1) (transclusion) (← links)
- Doubling identity for sinh (2) (transclusion) (← links)
- Doubling identity for cosh (1) (transclusion) (← links)
- Doubling identity for cosh (2) (transclusion) (← links)
- Doubling identity for cosh (3) (transclusion) (← links)
- Integral representation of Struve function (transclusion) (← links)
- Integral representation of Struve function (2) (transclusion) (← links)
- Integral representation of Struve function (3) (transclusion) (← links)
- Recurrence relation for Struve fuction (transclusion) (← links)
- Recurrence relation for Struve function (2) (transclusion) (← links)
- Derivative of Struve H0 (transclusion) (← links)
- 2cos(mt)cos(nt)=cos((m+n)t)+cos((m-n)t) (transclusion) (← links)
- Orthogonality relation for cosine on (0,pi) (transclusion) (← links)
- Orthogonality of Chebyshev T on (-1,1) (transclusion) (← links)
- Matrix exponential (transclusion) (← links)
- D/dz(z^(nu)H (nu))=z^(nu)H (nu-1) (transclusion) (← links)
- D/dz(z^(-nu)H (nu))=1/(sqrt(pi)2^(nu)Gamma(nu+3/2))-z^(-nu)H (nu+1) (transclusion) (← links)
- H (nu)(x) geq 0 for x gt 0 and nu geq 1/2 (transclusion) (← links)
- H (-(n+1/2))(z)=(-1)^n J (n+1/2)(z) for integer n geq 0 (transclusion) (← links)
- H (1/2)(z)=sqrt(2/(pi z))(1-cos(z)) (transclusion) (← links)
- H (3/2)(z)=sqrt(z/(2pi))(1+2/z^2)-sqrt(2/(pi z))(sin(z)+cos(z)/z) (transclusion) (← links)
- Li 2(z)+Li 2(1-z)=pi^2/6-log(z)log(1-z) (transclusion) (← links)
- K(m)=(pi/2)2F1(1/2,1/2;1;m) (transclusion) (← links)
- E(m)=(pi/2)2F1(-1/2,1/2;1;m) (transclusion) (← links)
- Nth derivative of logarithm (transclusion) (← links)
- Antiderivative of the logarithm (transclusion) (← links)
- 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 (transclusion) (← links)
- Gamma'(z)/Gamma(z)=-gamma-1/z+Sum z/(k(z+k)) (transclusion) (← links)
- Matrix e^A=limit of (I+A/s)^s (transclusion) (← links)
- Euler numbers (transclusion) (← links)
- Euler E n'(x)=nE n-1(x) (transclusion) (← links)
- Z coth(z) = 2z/(e^(2z)-1) + z (transclusion) (← links)
- Z coth(z) = sum of 2^(2n)B (2n) z^(2n)/(2n)! (transclusion) (← links)
- Z coth(z) = 2 Sum of (-1)^(n+1) zeta(2n) z^(2n)/pi^(2n) (transclusion) (← links)
- Generating function for Laguerre L (transclusion) (← links)
- L n(x)=(e^x/n!)d^n/dx^n(x^n e^(-x)) (transclusion) (← links)
- L n(0)=1 (transclusion) (← links)
- L n'(0)=-n (transclusion) (← links)
- Orthogonality of Laguerre L (transclusion) (← links)
- (n+1)L (n+1)(x) = (2n+1-x)L n(x)-nL (n-1)(x) (transclusion) (← links)
- XL n'(x)=nL n(x)-n L (n-1)(x) (transclusion) (← links)
- L n'(x)=-Sum L k(x) (transclusion) (← links)
- T n(x)=(1/2)(x+i sqrt(1-x^2))^n+(1/2)(x-i sqrt(1-x^2))^n (transclusion) (← links)
- U n(x)=(-i/2)(x+i sqrt(1-x^2))^n+(-i/2)(x-i sqrt(1-x^2))^n (transclusion) (← links)
- T n(x)=Sum (-1)^k n!/((2k)! (n-2k)!) (1-x^2)^k x^(n-2k) (transclusion) (← links)
- U n(x)=Sum (-1)^k n!/((2k+1)!(n-2k-1)!)(1-x^2)^(k+1/2)x^(n-2k-1) (transclusion) (← links)
- Ei(x)=-Integral from -x to infinity of e^(-t)/t dt (transclusion) (← links)