Article
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Using Beta Function and Factorization to Find New π-Series
Version 1
: Received: 11 November 2023 / Approved: 13 November 2023 / Online: 13 November 2023 (14:14:01 CET)
How to cite: Guo-Jie, L. Using Beta Function and Factorization to Find New π-Series. Preprints 2023, 2023110762. https://doi.org/10.20944/preprints202311.0762.v1 Guo-Jie, L. Using Beta Function and Factorization to Find New π-Series. Preprints 2023, 2023110762. https://doi.org/10.20944/preprints202311.0762.v1
Abstract
Using the method of the beta function, Sun has recently evaluated some series of the type $\sum_{k=0}^{\infty}(ak+b)x^k/\binom{mk}{nk}$.
By factorization of the polynomial $t^{m-n}(1-t)^n-x$, we will give a general method to find new $\pi$-series.
Keywords
Beta Function; Polynomial Factorization; Convergence
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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