Functions and Analysis

    

Miscellaneous Summation, Integration, and Transformation Formulas

Authors: Martin Nicholson

This is a discussion of miscellaneous summation, integration and transformation formulas obtained using Fourier analysis. The topics covered are: Series of the form $sum_{ninmathbb{Z}} c_ne^{pi i gamma n^2}$; Fusion of integrals, and in particular fusion of $q$-beta integrals related to Gauss-Fourier transform, and a related family of eigenfunctions of the cosine Fourier transform; Summation formulas of the type $sum_{nge 1}frac{chi(n)}{n},varphi(n)$ with Dirichlet characters; Trigonometric Fourier series expansion of hypergeometric functions of the argument $sin^2x$; Modifications of the inverse tangent integral and identities for corresponding infinite products.

Comments: 16 Pages.

Download: PDF

Submission history

[v1] 2024-04-15 18:50:22

Unique-IP document downloads: 598 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus