Abstract
This is a collection of definite integrals involving the logarithmic and polynomial functions in terms of special functions and fundamental constants. All the results in this work are new.
Highlights
The Logarithmic transform proposed by Reynolds and Stauffer [1] is used in this work and applied to a form of the Euler integral of the first kind and expressed in terms of the Lerch function
The Lerch function being a special function has the fundamental property of analytic continuation, which enables us to widen the range of evaluation for the parameters involved in our definite integral
We used our contour integral method to derive the logarithmic transform in terms of the Lerch function
Summary
The Logarithmic transform proposed by Reynolds and Stauffer [1] is used in this work and applied to a form of the Euler integral of the first kind and expressed in terms of the Lerch function. The authors used their contour integral method and applied it to a special case of the Beta function in [2] to derive a definite integral and expressed its closed form in terms of a special function. This derived integral formula was used to provide formal derivations in terms of special functions and fundamental constants and summarized in a Table.
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