Pages that link to "Mathematician:Fritz Oberhettinger"
The following pages link to Mathematician:Fritz Oberhettinger:
View (previous 50 | next 50) (20 | 50 | 100 | 250 | 500)- 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)
- Integral of (1+bt^z)^(-y)t^x dt = (1/z)*b^(-(x+1)/z) B((x+1)/z,y-(x+1)/z) (← links)
- Integral of t^(x-1)(1-t^z)^(y-1) dt=(1/z)B(x/z,y) (← links)
- Integral of (1+t)^(2x-1)(1-t)^(2y-1)(1+t^2)^(-x-y)dt=2^(x+y-2)B(x,y) (← links)
- Li2(z)=zPhi(z,2,1) (← links)
- Li 2(z)=-Li 2(1/z)-(1/2)(log z)^2 + i pi log(z) + pi^2/3 (← links)
- Book:Wilhelm Magnus/Formulas and Theorems for the Special Functions of Mathematical Physics/Third Edition (← links)
- Euler numbers (← links)
- Euler E n'(x)=nE n-1(x) (← links)
- Z coth(z) = 2z/(e^(2z)-1) + z (← links)
- Z coth(z) = sum of 2^(2n)B (2n) z^(2n)/(2n)! (← links)
- Z coth(z) = 2 Sum of (-1)^(n+1) zeta(2n) z^(2n)/pi^(2n) (← links)