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AIMS Mathematics

2020, Volume 5, Issue 6: 5724-5733. doi: 10.3934/math.2020367
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Research article

Definite integrals involving product of logarithmic functions and logarithm of square root functions expressed in terms of special functions

  • Department of Mathematics, York University, 4700 Keele Street, Toronto, M3J1P3, Canada
  • Received: 02 June 2020 Accepted: 06 July 2020 Published: 09 July 2020

  • MSC : 01A55, 11M06, 11M35, 30-02, 30D10, 30D30, 30E20

  • 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 $\int_{0}^{\infty}\ln^k(\alpha y)\ln(R(y))dy$ in terms of a special function, where $R(y)$ is a general function and $k$ and $\alpha$ are arbitrary complex numbers.

    Citation: Robert Reynolds, Allan Stauffer. Definite integrals involving product of logarithmic functions and logarithm of square root functions expressed in terms of special functions[J]. AIMS Mathematics, 2020, 5(6): 5724-5733. doi: 10.3934/math.2020367

    Related Papers:

  • 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 $\int_{0}^{\infty}\ln^k(\alpha y)\ln(R(y))dy$ in terms of a special function, where $R(y)$ is a general function and $k$ and $\alpha$ are arbitrary complex numbers.


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    [8] R. Reynolds, A. Stauffer, A Method for Evaluating Definite Integrals in terms of Special Functions with Examples, Available from: https://arxiv.org/pdf/1906.04927.pdf.
    [9] H. J. Weber, G. B. Arfken, Mathematical Methods for Physicists, ISE. Academic Press, 2004.
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  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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