Uniform approximations of the first symmetric elliptic integral in terms of elementary functions

被引：0
|
作者：
Bujanda, Blanca [1 ,2 ]
Lopez, Jose L. [1 ,2 ]
Pagola, Pedro J. [1 ,2 ]
Palacios, Pablo [1 ,2 ]
机构：
[1] Univ Publ Navarra, Dept Estadist Informat & Matemat, Pamplona, Spain
[2] Univ Publ Navarra, INAMAT2, Pamplona, Spain
来源：
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2022年 / 116卷 / 01期
关键词：
Symmetric standard elliptic integrals; Convergent expansions; Uniform expansions; Error bounds; ASYMPTOTIC EXPANSIONS; CONVERGENT EXPANSIONS; TABLE; INEQUALITIES; BOUNDS;
D O I：
10.1007/s13398-021-01151-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the standard symmetric elliptic integral R-F (x, y, z) for complex x, y, z. We derive convergent expansions of RF (x, y, z) in terms of elementary functions that hold uniformly for one of the three variables x, y or z in closed subsets (possibly unbounded) of C\(-infinity, 0]. The expansions are accompanied by error bounds. The accuracy of the expansions and their uniform features are illustrated by means of some numerical examples.
引用
收藏
页数：17
相关论文
共 37 条
  • [1] Uniform approximations of the first symmetric elliptic integral in terms of elementary functions
    Blanca Bujanda
    José L. López
    Pedro J. Pagola
    Pablo Palacios
    Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2022, 116
  • [2] An Analytic Representation of the Second Symmetric Standard Elliptic Integral in Terms of Elementary Functions
    Bujanda, Blanca
    Lopez, Jose L.
    Pagola, Pedro J.
    Palacios, Pablo
    RESULTS IN MATHEMATICS, 2022, 77 (04)
  • [3] An Analytic Representation of the Second Symmetric Standard Elliptic Integral in Terms of Elementary Functions
    Blanca Bujanda
    José L. López
    Pedro J. Pagola
    Pablo Palacios
    Results in Mathematics, 2022, 77
  • [4] Uniform Convergent Expansions of the Error Function in Terms of Elementary Functions
    Ferreira, Chelo
    Lopez, Jose L.
    Sinusia, Ester Perez
    MEDITERRANEAN JOURNAL OF MATHEMATICS, 2023, 20 (03)
  • [5] UNIFORM REPRESENTATIONS OF THE INCOMPLETE BETA FUNCTION IN TERMS OF ELEMENTARY FUNCTIONS
    Ferreira, Chelo
    Lopez, Jose L.
    Perez Sinusia, Ester
    ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, 2018, 48 : 450 - 461
  • [6] Uniform Convergent Expansions of the Error Function in Terms of Elementary Functions
    Chelo Ferreira
    José L. López
    Ester Pérez Sinusía
    Mediterranean Journal of Mathematics, 2023, 20
  • [7] Uniform convergent expansions of the Gauss hypergeometric function in terms of elementary functions
    Ferreira, Chelo
    Lopez, Jose L.
    Perez Sinusia, Ester
    INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2018, 29 (12) : 942 - 954
  • [8] Convergent expansions of the Bessel functions in terms of elementary functions
    Lopez, Jose L.
    ADVANCES IN COMPUTATIONAL MATHEMATICS, 2018, 44 (01) : 277 - 294
  • [9] Convergent expansions of the Bessel functions in terms of elementary functions
    José L. López
    Advances in Computational Mathematics, 2018, 44 : 277 - 294
  • [10] Sharp approximations for the generalized elliptic integral of the first kind
    He, Zai-Yin
    Jiang, Yue-Ping
    Wang, Miao-Kun
    MATHEMATICA SLOVACA, 2023, 73 (02) : 425 - 438
1234