Pages that link to "Book:Arthur Erdélyi/Higher Transcendental Functions Volume I"
The following pages link to Book:Arthur Erdélyi/Higher Transcendental Functions Volume I:
View (previous 20 | next 20) (20 | 50 | 100 | 250 | 500)- 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) (← links)
- 1Phi0(a;;z) as infinite product (← links)
- 1Phi0(a;;z)1Phi0(b;;az)=1Phi0(ab;;z) (← links)
- (z/(1-q))2Phi1(q,q;q^2;z)=Sum z^k/(1-q^k) (← links)
- 2Phi1(q,-1;-q;z)=1+2Sum z^k/(1+q^k) (← links)
- Z/(1-sqrt(q))2Phi1(q,sqrt(q);sqrt(q^3);z)=Sum z^k/(1-q^(k-1/2)) (← links)
- B(x,y)=integral (t^(x-1)+t^(y-1))(1+t)^(-x-y) dt (← links)
- B(x,y+1)=(y/x)B(x+1,y) (← links)
- B(x,y+1)=(y/(x+y))B(x,y) (← links)
- B(x,y)B(x+y,z)=B(y,z)B(y+z,x) (← links)
- B(x,y)B(x+y,z)=B(z,x)B(x+z,y) (← 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) (← links)
- 1/B(n,m)=m((n+m-1) choose (n-1)) (← links)
- 1/B(n,m)=n((n+m-1) choose (m-1)) (← 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 (← links)
- Integral t^(x-1)(1-t)^(y-1)(1+bt)^(-x-y)dt = (1+b)^(-x)B(x,y) (← links)
- Integral t^(x-1)(1+bt)^(-x-y) dt = b^(-x) B(x,y) (← links)
- Integral (t-b)^(x-1)(a-t)^(y-1)dt=(a-b)^(x+y-1)B(x,y) (← 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) (← 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) (← links)