Special Functions and Their Application / Bipin Singh Koranga, Vivek Kumar Nautiyal, Sanjay Kumar Padaliya.

Format:

Book

Author/Creator:

Koranga, Bipin Singh, author.

Nautiyal, Vivek Kumar, author.

Padaliya, Sanjay Kumar, author.

Series:

River Publishers Series in Mathematical and Engineering Sciences.

River Publishers series in mathematical and engineering sciences

Language:

English

Subjects (All):

Functions, Special.

Physical Description:

1 online resource (124 pages)

Edition:

First edition.

Place of Publication:

Gistrup, Denmark : River Publishers, [2021]

Summary:

This short text gives clear descriptions and explanations of the Gamma function, the Probability Integral and its related functions, Spherical Harmonics Theory, The Bessel function, Hermite polynomials and Laguerre polynomials.

Contents:

Front Cover

Special Functions and their Applications

Contents

Preface

List of Tables

1 The Gamma Function

1.1 Definition of Gamma Function

1.2 Gamma Function and Some Relations

1.3 The Logarithmic Derivative of the Gamma Function

1.4 Asymptotic Representation of the Gamma Function for Large |z|

1.5 Definite Integrals Related to the Gamma Function

1.6 Exercises

2 The Probability Integral and Related Functions

2.1 The Probability Integral and its Basic Properties

2.2 Asymptotic Representation of Probability Integral for Large |z|

2.3 The Probability Integral of Imaginary Argument

2.4 The Probability Fresnel Integrals

2.5 Application to Probability Theory

2.6 Application to the Theory of Heat Conduction

2.7 Application to the Theory of Vibrations

2.8 Exercises

3 Spherical Harmonics Theory

3.1 Introduction

3.2 The Hypergeometric Equation and its Series Solution

3.3 Legendre Functions

3.4 Integral Representations of the Legendre Functions

3.5 Some Relations Satisfied by the Legendre Functions

3.6 Workskian of Pairs of Solutions of Legendre's Equation

3.7 Recurrence Relations for the Legendre Functions

3.8 Associated Legendre Functions

3.9 Exercises

4 Bessel Function

4.1 Bessel Functions

4.2 Generating Function

4.3 Recurrence Relations

4.4 Orthonormality

4.5 Application to the Optical Fiber

4.6 Exercises

5 Hermite Polynomials

5.1 Hermite Functions

5.2 Generating Function

5.3 Recurrence Relations

5.4 Rodrigues Formula

5.5 Orthogonality and Normalilty

5.6 Application to the Simple Harmonic Oscillator

5.7 Exercises

6 Laguerre Polynomials

6.1 Laguerre Functions

6.2 Generating Function

6.3 Recurrence Relations

6.4 Rodrigues Formula

6.5 Orthonormality

6.6 Application to the Hydrogen Atom.

6.7 Associated Laguerre Polynomials

6.7.1 Properties of Associated Laguerre Polynomials

6.8 Exercises

Bibliography

Index

About the Authors

Back Cover.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9781000792270

1000792277

9781003339595

100333959X

9781000795592

1000795594

9788770226257

8770226253

OCLC:

1289259031

Publisher Number:

9781003339595