| viXra.org > Functions and Analysis > 2404 |
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| viXra.org > Functions and Analysis > 2404 |
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[2] viXra:2404.0072 [pdf] submitted on 2024-04-15 18:50:22
Authors: Martin Nicholson
Comments: 16 Pages.
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.
Category: Functions and Analysis
[1] viXra:2404.0009 [pdf] submitted on 2024-04-02 20:00:41
Authors: A. V. Serghienko
Comments: 3 Pages.
We derive the formulae for the sine and the cosine of the sum, not using the notions of scalar and vector products, and using only the definitions of the sine and the cosine. We derive the formulae for the gradient operator, the divergence and the Laplace operator in different orthogonal coordinate systems, not using any additional constructions like Lame coefficients, and using only the definitions of the sine and the cosine.
Category: Functions and Analysis
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