![sum_(k=0)^(infty)[((m)_k)/(k!)]^3](/images/equations/MorleysFormula/Inline1.svg) |  | ![1+(m/1)^3+[(m(m+1))/(1·2)]^3+...](/images/equations/MorleysFormula/Inline3.svg) |
(1)
|
 |  | ![(Gamma(1-3/2m))/([Gamma(1-1/2m)]^3)cos(1/2mpi),](/images/equations/MorleysFormula/Inline6.svg) |
(2)
|
where 
is a Pochhammer symbol and 
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).](/images/equations/MorleysFormula/NumberedEquation1.svg) |
(3)
|
Morley's Formula
See also
Gamma FunctionExplore with Wolfram|Alpha
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 FormulaCite this as:
Weisstein, Eric W. "Morley's Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MorleysFormula.html