Bieberbacj Conjecture

Author

Eric W. Weisstein
April 15, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/ComplexAnalysis/BieberbachConjecture.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/BieberbachConjecture.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Sum

(∑_(j=k)^n)(((-1))^(j+k)) (e^(-j t)) (Binomial[2 j, j-k]) (Binomial[j+n+1, n-j])==(((-1))^(2 k)) (e^(-k t)) (Binomial[k+n+1, n-k]) (Subscript[, 3])(Subscript[F, 2])(k+(1/2),k-n,k+n+2;k+(3/2),2 k+1;(e^(-t)))

V5

FullSimplify[Sum[(-1)^(k+j)Binomial[2j,j-k]Binomial[n+j+1,n-j]Exp[-j t],{j,k,n}],(k|k|n)∈Integers]

V7

Sum[(-1)^(k+j)Binomial[2j,j-k]Binomial[n+j+1,n-j]Exp[-j t],{j,k,n}]

FullSimplify[%]

TraditionalForm[%]