تقرير
General Berndt-Type Integrals and Series Associated with Jacobi Elliptic Functions
| العنوان: | General Berndt-Type Integrals and Series Associated with Jacobi Elliptic Functions |
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| المؤلفون: | Xu, Ce, Zhao, Jianqiang |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 05A30, 32A27, 42A16, 33E05, 11B68 |
| الوصف: | In this paper, we prove two structural theorems on the general Berndt-type integrals with the denominator having arbitrary positive degrees by contour integrations involving hyperbolic and trigonometric functions, and hyperbolic sums associated with Jacobi elliptic functions. We first establish explicit relations between these integrals and four classes of hyperbolic sums. Then, using our previous results on hyperbolic series and applying the matrix method from linear algebra, we compute explicitly several general hyperbolic sums and their higher derivatives. These enable us to express two families of general Berndt-type integrals as polynomials in $\Gamma^4(1/4)$ and $\pi^{-1}$ with rational coefficients, where $\Gamma$ is the Euler gamma function. At the end of the paper, we provide some conjectures of general Berndt-type integrals. Comment: arXiv admin note: text overlap with arXiv:2311.15666 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2401.01385 |
| رقم الأكسشن: | edsarx.2401.01385 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |