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.
Highlights
The main purpose of this work is to establish a new method which can be used to evaluate theR ∞ ym logk integral 01+αyn dy in the form of a special function, where k, α, a, m and n are arbitrary complex numbers subject to the restrictions given
This is a novel approach to these problems in mathematics and has been used by us in [1]. This method involves using a form of the Cauchy integral formula
Both the definite integral and special function can be written in terms of the same contour integral, and we can equate the two
Summary
The main purpose of this work is to establish a new method which can be used to evaluate the. 1+αyn dy in the form of a special function, where k, α, a, m and n are arbitrary complex numbers subject to the restrictions given. This is a novel approach to these problems in mathematics and has been used by us in [1]. This method involves using a form of the Cauchy integral formula. Both the definite integral and special function can be written in terms of the same contour integral, and we can equate the two. The integral can be thought of as a Mellin transform, which has been extensively tabulated
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