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Bradley's Theorem

Let

S(alpha,beta,m;z)=msum_(j=0)^infty(Gamma(m+j(z+1))Gamma(beta+1+jz))/(Gamma(m+jz+1)Gamma(alpha+beta+1+j(z+1)))((alpha)_j)/(j!),

where (alpha)_j is a Pochhammer symbol, and let alpha be a negative integer. Then

S(alpha,beta,m;z)=(Gamma(beta+1-m))/(Gamma(alpha+beta+1-m)),

where Gamma(z) is the gamma function.

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References

Berndt, B. C. Ramanujan's Notebooks, Part IV. New York: Springer-Verlag, pp. 346-348, 1994.Bradley, D. "On a Claim by Ramanujan about Certain Hypergeometric Series." Proc. Amer. Math. Soc. 121, 1145-1149, 1994.

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Bradley's Theorem

Cite this as:

Weisstein, Eric W. "Bradley's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BradleysTheorem.html

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