A master integral in four parameters

作者：Sofo Anthony^*

来源：Journal of Mathematical Analysis and Applications, 2017, 448(1): 81-92.

DOI：10.1016/j.jmaa.2016.10.073

• Integral representation
• Hypergeometric functions
• Lerch transcendent
• Hurwitz zeta function
• Partial fraction approach
• Harmonic number

In this paper we consider a master integral in four arbitrary parameters. The integrand involves the logarithmic function and the Gauss hypergeometric function, which in certain special cases the integral reduces to identities involving zeta functions. A relationship will also be created between the integral and Euler sums of arbitrary order and arbitrary argument. Many interesting new specific examples will be highlighted.

• 出版日期2017-4-1