On differentiation with respect to parameters of the functions of the Mittag-Leffler type

被引：2

作者：

Rogosin, Sergei V. ^{[1
]}

Giraldi, Filippo ^{[2
,3
]}

Mainardi, Francesco ^{[4
,5
]}

机构：

[1] Belarusian State Univ, Dept Econ, Nezavisimosti Ave 4, Minsk 220030, BELARUS

[2] Int Telematic Univ Uninettuno, Sect Math, Rome, Italy

[3] Univ KwaZulu Natal, Sch Chem & Phys, Durban, South Africa

[4] Univ Bologna, Dept Phys & Astron, Bologna, Italy

[5] INFN, Bologna, Italy

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2025年 / 36卷 / 05期

关键词：

Mittag-Leffler function; Le Roy-type function; differentiation; Mellin-Barnes integral; BESSEL-FUNCTIONS; DERIVATIVES; ORDER;

D O I：

10.1080/10652469.2024.2428850

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The formal term-by-term differentiation with respect to parameters is demonstrated to be legitimate for the Mittag-Leffler-type functions. The justification of differentiation formulas is made by using the concept of the uniform convergence. This approach is applied to the Mittag-Leffler function depending on two parameters and, additionally, for the three-parametric Mittag-Leffler functions (namely, for the Prabhakar function and the Le Roy-type function), as well as for the four-parametric Mittag-Leffler function (and, in particular, for the Wright function). The differentiation with respect to the involved parameters is discussed also in case those special functions which are represented via the Mellin-Barnes integrals.

引用

页码：400 / 412

页数：13

共 31 条

[1] On some inequalities for the gamma and psi functions [J].

Alzer, H .

MATHEMATICS OF COMPUTATION, 1997, 66 (217) :373-389

[2] INTEGRAL-REPRESENTATIONS OF DERIVATIVES AND INTEGRALS WITH RESPECT TO THE ORDER OF THE BESSEL-FUNCTIONS JV(T),IV(T), THE ANGER FUNCTION JV(T) AND THE INTEGRAL BESSEL-FUNCTION JIV(T) [J].

APELBLAT, A ;

KRAVITSKY, N .

IMA JOURNAL OF APPLIED MATHEMATICS, 1985, 34 (02) :187-210

[3] INTEGRAL-REPRESENTATION OF KELVIN FUNCTIONS AND THEIR DERIVATIVES WITH RESPECT TO THE ORDER [J].

APELBLAT, A .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1991, 42 (05) :708-714

[4] Differentiation of the Wright Functions with Respect to Parameters and Other Results [J].

Apelblat, Alexander ;

Mainardi, Francesco .

APPLIED SCIENCES-BASEL, 2022, 12 (24)

[5] Differentiation of the Mittag-Leffler Functions with Respect to Parameters in the Laplace Transform Approach [J].

Apelblat, Alexander .

MATHEMATICS, 2020, 8 (05)

[6] Asymptotic analysis of three-parameter Mittag-Leffler function with large parameters, and application to sub-diffusion equation involving Bessel operator [J].

Askari, Hassan ;

Ansari, Alireza .

FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2024, 27 (03) :1162-1185

[7]

Bateman H., 1954, TABLES INTEGRALS TRA

[8] Higher derivatives of the Bessel functions with respect to the order [J].

Brychkov, Yu. A. .

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2016, 27 (07) :566-577

[9] On the Order Derivatives of Bessel Functions [J].

Dunster, T. M. .

CONSTRUCTIVE APPROXIMATION, 2017, 46 (01) :47-68

[10]

Garra Roberto, 2019, WSEAS Transactions on Mathematics, V18, P428

← 1 2 3 4 →