A double Stirling formula

Authors:
J. R. Quine and Richard R. Song

Journal:
Proc. Amer. Math. Soc. **119** (1993), 373-379

MSC:
Primary 11F20; Secondary 11E45, 11M41

MathSciNet review:
1164151

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Abstract: We give an asymptotic expansion as of , where the product is over . The formula is analogous to the classical Stirling expansion on . Of special interest is the constant term in the expansion, which involves the Dedekind eta function . Finding this constant is related to the Kronecker limit formula for the derivative at 0 of the zeta function . We consider instead the zeta function without absolute values.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1993-1164151-5

Keywords:
Stirling expansion,
Dedekind eta function,
Kronecker limit formula,
zeta regularized product

Article copyright:
© Copyright 1993
American Mathematical Society