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On generalized gamma functions related to the Laurent coefficients of the Riemann zeta function

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Summary

We study a class of generalized gamma functions Г k (z) which relate to the generalized Euler constantsγ k (basically the Laurent coefficients ofζ(s)) as Г(z) does to the Euler constantγ. A new series expansion forγ k is derived, and the constant term in the asymptotic expansion for log Г k (z) is studied in detail. These and related constants are numerically computed for 1 ≤k ≤ 15.

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Authors and Affiliations

  1. Department of Mathematics, Statistics and Computing Science, Dalhousie University, B3H 3H5, Halifax, Nova Scotia, Canada

    Karl Dilcher

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  1. Karl Dilcher
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Dilcher, K. On generalized gamma functions related to the Laurent coefficients of the Riemann zeta function. Aeq. Math. 48, 55–85 (1994). https://doi.org/10.1007/BF01837979

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  • DOI: https://doi.org/10.1007/BF01837979

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