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A Definite Integral Involving the Logarithmic Function in Terms of the Lerch Function

Author

Listed:
  • Robert Reynolds

    (Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada)

  • Allan Stauffer

    (Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada)

Abstract

We present a method using contour integration to evaluate the definite integral of the form ∫ 0 ∞ log k ( a y ) R ( y ) d y in terms of special functions, where R ( y ) = y m 1 + α y n and k , m , a , α and n are arbitrary complex numbers. We use this method for evaluation as well as to derive some interesting related material and check entries in tables of integrals.

Suggested Citation

  • Robert Reynolds & Allan Stauffer, 2019. "A Definite Integral Involving the Logarithmic Function in Terms of the Lerch Function," Mathematics, MDPI, vol. 7(12), pages 1-5, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1148-:d:290331
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