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Derivation of Logarithmic and Logarithmic Hyperbolic Tangent Integrals Expressed in Terms of Special Functions

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

The derivation of integrals in the table of Gradshteyn and Ryzhik in terms of closed form solutions is always of interest. We evaluate several of these definite integrals of the form ∫ 0 ∞ log ( 1 ± e − α y ) R ( k , a , y ) d y in terms of a special function, where R ( k , a , y ) is a general function and k , a and α are arbitrary complex numbers, where R e ( α ) > 0 .

Suggested Citation

  • Robert Reynolds & Allan Stauffer, 2020. "Derivation of Logarithmic and Logarithmic Hyperbolic Tangent Integrals Expressed in Terms of Special Functions," Mathematics, MDPI, vol. 8(5), pages 1-6, May.
  • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:687-:d:352946
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