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Some Special Srinivasa Aiyangar Ramanujan's Series and Formulas
(1887-1920)
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where 
and for each positive integer k, 
and for each positive integer k, 
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, for all 
, where 
is the Gamma Function.
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Define
, which is called Ramanujan Theta Function. Special values include
.- Hypergeometric Identity
.- Ramanujan’s Master Theorem
then
for small of x = 0.Series Collections
References
Berndt, B. C. Ramanujan's Notebooks: Part I. New York: Springer-Verlag, 1985.
Berndt, B. C. Ramanujan's Notebooks: Part II. New York: Springer-Verlag, 1989.
Berndt, B. C. Ramanujan's Notebooks, Part IV. New York: Springer-Verlag, 1994.
Berndt, B. C. and Bhargava, S. ``A Remarkable Identity Found in Ramanujan's Third Notebook.'' Glasgow Math. J, 1992.
D.V. Chudnovsky and G.V. Chudnovsky. Approxiamtions and Complex Multiplication According to Ramanujan. San Diego, CA: Academic Press, 1988.
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