Let
be any function, say analytic or integrable. Then
|
(1)
|
and
|
(2)
|
where
is the Dirichlet lambda function and
is the gamma function. Equation (◇) is obtained
from (◇) by defining
|
(3)
|
These formulas give valid results only for certain classes of functions, and are connected with Mellin transforms (Hardy 1999,
p. 15).
See also
Ramanujan's Master Theorem
Portions of this entry contributed by Jonathan Sondow (author's
link)
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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. 15 and 186-195, 1999.Referenced on Wolfram|Alpha
Ramanujan's Interpolation
Formula
Cite this as:
Sondow, Jonathan and Weisstein, Eric W. "Ramanujan's Interpolation Formula." From MathWorld--A
Wolfram Web Resource. https://mathworld.wolfram.com/RamanujansInterpolationFormula.html
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