Special Functions of Mathematics for EngineersModern engineering and physical science applications demand a thorough knowledge of applied mathematics, particularly special functions. These typically arise in applications such as communication systems, electro-optics, nonlinear wave propagation, electromagnetic theory, electric circuit theory, and quantum mechanics. This text systematically introduces special functions and explores their properties and applications in engineering and science. |
Contents
Infinite Series Improper Integrals and Infinite Products | 1 |
The Gamma Function and Related Functions | 61 |
Contents | 87 |
Other Functions Defined by Integrals | 109 |
Legendre Polynomials and Related Functions | 141 |
Bessel Functions | 237 |
Bessel Functions of Other Kinds | 287 |
Contents | 308 |
Applications Involving Bessel Functions | 323 |
The Hypergeometric Function | 357 |
The Confluent Hypergeometric Functions | 385 |
Generalized Hypergeometric Functions | 411 |
Applications Involving HypergeometricType Functions | 429 |
| 451 | |
Selected Answers to Exercises | 469 |
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Common terms and phrases
addition applications associated assume asymptotic formulas asymptotic series becomes Bessel functions boundary called coefficients condition consider constant continuous deduce defined definition denote derive determine developed differential directly discussion distribution diverges equation evaluate Example Exercises expand expression Finally finite follows formula Fourier gamma function given Hence Hermite hypergeometric function identity important independent integral integral representation interval introduced involving Laguerre leads Legendre polynomials limit linear observation obtain partial particular positive potential properties recall recurrence formula reduces relation replace respectively result of problem satisfy second kind series representation Show shown side solution solving special functions spherical substitution taking temperature Theorem theory transform values verify write yields zero