代数方程超几何解中涉及特殊函数的恒等式

IF 0.8 4区数学 Q2 MATHEMATICS

Turkish Journal of Mathematics Pub Date : 2023-09-25 DOI:10.55730/1300-0098.3464

JUAN LUIS GONZALEZ-SANTANDER

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引用次数: 0

摘要

从$x^{m}-x+t=0$对于$m=2,3,4$的代数解及其对应的超几何函数解出发，得到了一组超几何函数的约简公式。通过对这些结果的微分和积分，并应用其他已知的超几何函数的约简公式，导出了新的特殊函数的约简公式，以及一些初等函数定积分的计算。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Identities involving special functions from hypergeometric solution of algebraic equations

From the algebraic solution of $x^{m}-x+t=0$ for $m=2,3,4$ and the corresponding solution in terms of hypergeometric functions, we obtain a set of reduction formulas for hypergeometric functions. By differentiation and integration of these results, and applying other known reduction formulas of hypergeometric functions, we derive new reduction formulas of special functions as well as the calculation of some definite integrals in terms of elementary functions.

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来源期刊

Turkish Journal of Mathematics 数学-数学

CiteScore

1.80

自引率

10.00%

发文量

161

审稿时长

6-12 weeks

期刊介绍： The Turkish Journal of Mathematics is published electronically 6 times a year by the Scientific and Technological Research Council of Turkey (TÜBİTAK) and accepts English-language original research manuscripts in the field of mathematics. Contribution is open to researchers of all nationalities.