Special Integrals / by Abhishek Mishra.

Format:

Book

Author/Creator:

Mishra, Abhishek.

Series:

University Texts in the Mathematical Sciences, 2731-9326

Language:

English

Subjects (All):

Integral equations.

Mathematical analysis.

Integral Equations.

Integral Transforms and Operational Calculus.

Local Subjects:

Integral Equations.

Integral Transforms and Operational Calculus.

Physical Description:

1 online resource (288 pages)

Edition:

1st ed. 2025.

Place of Publication:

Singapore : Springer Nature Singapore : Imprint: Springer, 2025.

Summary:

Targeted to upper-undergraduate and graduate students of mathematics, this book discusses special integrals and their applications in finding certain series sums. It starts with the differentiation and the integration methods for summing a series that is applied to find the sum of various binomial and trigonometrical series. It also discusses methods to find the sum of series involving the variables having exponents in integral or fractional powers of 2. Complex variables are freely used to derive several theorems, which result in several special integrals and series sums. Bessel coefficients, Bessel functions, and their various generalizations are also discussed in the book. As a particular case of generalized Bessel functions, pseudo-exponential functions are defined, and their properties are studied in the book. Broadly divided into two parts—Part 1 and Part 2—the book has six chapters in Part 1, whereas Part 2 has six chapters on solutions to the problems in Part 1. To understand the topics in the book, the minimum prerequisites are the knowledge of calculus, complex analysis, and Fourier series.

Contents:

Binomial Series

Trigonometrical Series

Special Integrals

Pseudo-Exponential Functions

Series Sums using Special Integrals

Solutions to Binomial Series

Solutions to Trigonometrical Series.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9789819775149

9819775140

OCLC:

1512319182