On Generalized Complete (p, q)-Elliptic Integrals
نویسندگان
چکیده
In this paper, we study the generalized complete (p, q)-elliptic integrals of first and second kind as an application trigonometric functions with two parameters, establish monotonicity, convexity concavity these functions. particular, some Turán type inequalities are given. Finally, also show new series representations by applying Alzer Richard’s methods.
منابع مشابه
Integrals involving complete elliptic integrals
We give a closed-form evaluation of a number of Erd elyi-Kober fractional integrals involving elliptic integrals of the rst and second kind, in terms of the 3F2 generalized hypergeometric function. Reduction formulae for 3F2 enable us to simplify the solutions for a number of particular cases. c © 1999 Elsevier Science B.V. All rights reserved.
متن کاملON A q-ANALOGUE OF THE p-ADIC GENERALIZED TWISTED L-FUNCTIONS AND p-ADIC q-INTEGRALS
The purpose of this paper is to define generalized twisted q-Bernoulli numbers by using padic q-integrals. Furthermore, we construct a q-analogue of the p-adic generalized twisted L-functions which interpolate generalized twisted q-Bernoulli numbers. This is the generalization of Kim’s h-extension of p-adic q-L-function which was constructed in [5] and is a partial answer for the open question ...
متن کاملFast Computation of Complete Elliptic Integrals and Jacobian Elliptic Functions
As a preparation step to compute Jacobian elliptic functions efficiently, we created a fast method to calculate the complete elliptic integral of the first and second kinds, K(m) and E(m), for the standard domain of the elliptic parameter, 0 < m < 1. For the case 0 < m < 0.9, the method utilizes 10 pairs of approximate polynomials of the order of 9 to 19 obtained by truncating Taylor series exp...
متن کاملGeneralized Elliptic Integrals and Modular Equations
In geometric function theory, generalized elliptic integrals and functions arise from the Schwarz-Christoffel transformation of the upper half-plane onto a parallelogram and are naturally related to Gaussian hypergeometric functions. Certain combinations of these integrals also occur in analytic number theory in the study of Ramanujan’s modular equations and approximations to π. The authors stu...
متن کاملGeneralized elliptic-type integrals and asymptotic formulas
A number of families of elliptic-type integrals have been studied recently due to their importance and potential for applications in some problems of radiation physics. The object of this work is to present a unified and generalized form of such elliptic-type integrals and to study its properties, including recurrence formulas and asymptotic expansion.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Mathematica Scientia
سال: 2021
ISSN: ['1572-9087', '0252-9602']
DOI: https://doi.org/10.1007/s10473-021-0211-4