* uschian groups of the first kind * Automorphic forms and functions * Hecke operators and the zeta-functions associated with modular forms * Elliptic curves * Abelian extensions of imaginary quadratic fields and complex multiplication of elliptic curves * Modular functions of higher level * Zeta-functions of algebraic curves and abelian varieties * The cohomology group assoicated with cusp forms * Arithmetic Fuschian groups

Introduction to the arithmetic theory of automorphic functions

Integral transforms (Laplace, Fourier and Mellin) are introduced with their properties, the relationship between these transforms was discussed and some important applications in physics and engineering were given. ااااااا دقل مت ضارعتسإ ةساردو ل ةيلماكتلا تليوحتلا لك ، سلبل تلوحت نم روف ي ر نيليمو عم ةشقانم كلذكو ،اهنم لك صاوخ و صئاصخ ةقلعلا ةشقانم مت هذه نيب طبرلاو و ،تليوحتلا مت ميدقت تاقيبطتلا ضعب تليوحتلا هذهل ةمهملا يف تلاجم ءايزيفلا ةسدنهلاو.

Integral transforms and their applications

Discussion of the most important formulae and construction of plots for some functions of mathematical physics relevant to quantum mechanics. These functions are Hermite polynomials, Legendre polynomials and Legendre functions, spherical harmonics, Bessel functions and spherical Bessel functions and Laguerre polynomials. Directly related to some of these and also discussed are the eigenfunctions of the one-dimensional harmonic oscillator and the radial eigenfunctions of the harmonics oscillator in three dimensions and of the hydrogen atom.

Special Functions of Mathematical Physics

Confluent Hypergeometric Functions By Dr L J Slater Pp ix + 247 (Cambridge: At the University Press, 1960) 65s net

Confluent Hypergeometric Functions

/pdf/handbook-of-hypergeometric-integrals-26f24bii74.pdf

Handbook of Hypergeometric Integrals

In the theory of generalized hypergeometric functions, classical summation theorems for the series 2 F 1 , 3 F 2 , 4 F 3 , 5 F 4 and 7 F 6 play a key role. Very recently, Masjed-Jamei and Koepf established generalizations of the above-mentioned summation theorems. Inspired by their work, the main objective of the paper is to provide a new class of Laplace-type integrals involving generalized hypergeometric functions p F p for p = 2 , 3 , 4 , 5 and 7 in the most general forms. Several new and known cases have also been obtained as special cases of our main findings.

https://www.mdpi.com/2075-1680/8/3/87/pdf

On a New Class of Laplace-Type Integrals Involving Generalized Hypergeometric Functions

Very recently Masjed-Jamei and Koepf [Axioms 2018, 7 (2), 38] established interesting and useful generalizations of various classical summation theorems for the ${}_{2}F_{1}$, ${}_{3}F_{2}$, ${}_{4}F_{3}$, ${}_{5}F_{4}$ and ${}_{6}F_{5}$ generalized hypergeometric series. The main aim of this paper is to establish eleven Eulerian's type integrals involving generalized hypergeometric functions by employing these theorems. Several special cases (known and unknown) have also been given.

/pdf/evaluation-of-a-new-class-of-eulerian-s-type-integrals-1636n62j7w.pdf

Evaluation of a new class of eulerian's type integrals involving generalized hypergeometric functions

The aim of this note is to provide some new Gaussian hypergeometric summation formulae. These are further used to obtain certain new expressions for the product of hypergeometric series. Already ob...

On some new Gaussian hypergeometric summation formulae with applications

In this note, we aim to provide generalizations of (i) Knuth's old sum (or Reed Dawson identity) and (ii) Riordan's identity using a hypergeometric series approach.

Insuk Kim

Papers

On a New Class of Laplace-Type Integrals Involving Generalized Hypergeometric Functions

Evaluation of a new class of eulerian's type integrals involving generalized hypergeometric functions

On some new Gaussian hypergeometric summation formulae with applications

A note on a generalization of two well-known Cominatorial identities via a Hypergeometric series approach

The class number of orders in a quaternion algebra over a dyadic local field