Sharp inequalities for the complete elliptic integrals of the first and second kinds
نویسندگان
چکیده
By studying the monotonicity properties of K(r), E(r) and some combinations elementary functions special functions, new inequalities for complete elliptic integrals first second kinds are established. where K(r) =f0 ?/2
منابع مشابه
Some Bounds for the Complete Elliptic Integrals of the First and Second Kinds
In the article, the complete elliptic integrals of the first and second kinds are bounded by using the power series expansions of some functions, the celebrated Wallis inequality, and an integral inequality due to R. P. Agarwal, P. Cerone, S. S. Dragomir and F. Qi. Mathematics subject classification (2010): 26D15, 33C75, 33E05.
متن کاملNumerical computation of inverse complete elliptic integrals of first and second kinds
We developed the numerical procedures to evaluate the inverse functions of the complete elliptic integrals of the first and second kind, K(m) and E(m), with respect to the parameter m. The evaluation is executed by inverting eight sets of the truncated Taylor series expansions of the integrals in terms of m or of − log(1 −m). The developed procedures are (1) so precise that the maximum absolute...
متن کاملefl students gender and socioeconomic status: the use of politeness strategies in the first and second languages
within the components of communicative competence, a special emphasis is put on the “rules of politeness,” specifically the politeness strategies (brown and levinson, 1978) that speakers deploy when performing the request speech act. this is because the degree of imposition that making a request places upon one’s interlocutor(s) has been seen to be influenced by several factors among which, as ...
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 کاملInequalities and bounds for elliptic integrals
Computable lower and upper bounds for the symmetric elliptic integrals and for Legendre’s incomplete integral of the first kind are obtained. New bounds are sharper than those known earlier. Several inequalities involving integrals under discussion are derived. © 2007 Elsevier Inc. All rights reserved.
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: Applicable Analysis and Discrete Mathematics
سال: 2022
ISSN: ['1452-8630', '2406-100X']
DOI: https://doi.org/10.2298/aadm200613020j