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Morley's Formula


sum_(k=0)^(infty)[((m)_k)/(k!)]^3=1+(m/1)^3+[(m(m+1))/(1·2)]^3+...
(1)
=(Gamma(1-3/2m))/([Gamma(1-1/2m)]^3)cos(1/2mpi),
(2)

where (m)_k is a Pochhammer symbol and Gamma(z) is the gamma function. This is a special case of the identity

 sum_(k=0)^infty[((m)_k)/(k!)]^n=_nF_(n-1)(m,...,m_()_(n);1,...,1_()_(n-1);1).
(3)

See also

Gamma Function

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References

Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, pp. 104 and 111, 1999.

Referenced on Wolfram|Alpha

Morley's Formula

Cite this as:

Weisstein, Eric W. "Morley's Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MorleysFormula.html

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