Remarks on some integrals and series involving the Stirling numbers and $\zeta (n)$
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- by Li-Chien Shen PDF
- Trans. Amer. Math. Soc. 347 (1995), 1391-1399 Request permission
Abstract:
From the perspective of the well-known identity \[ {}_2{F_1}(a,b;c;1) = \frac {{\Gamma (c)\Gamma (c - a - b)}} {{\Gamma (c - a)\Gamma (c - b)}},\] we clarify the connections between the Stirling numbers $s_k^n$ and the Riemann zeta function $\zeta (n)$. As a consequence, certain series and integrals can be evaluated in terms of $\zeta (n)$ and $s_k^n$.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 347 (1995), 1391-1399
- MSC: Primary 11B73; Secondary 11M06, 11Y60, 33C05
- DOI: https://doi.org/10.1090/S0002-9947-1995-1257124-1
- MathSciNet review: 1257124