Special Integrals

• Verfasst von: Mishra, Abhishek [VerfasserIn]
• Titel: Special Integrals
• Verf.angabe: by Abhishek Mishra
• Ausgabe: 1st ed. 2025.
• Verlagsort: Singapore
• Verlag: Springer Nature Singapore
• Jahr: 2025
• Umfang: 1 Online-Ressource(XVI, 382 p. 7 illus., 1 illus. in color.)
• Gesamttitel/Reihe: University Texts in the Mathematical Sciences
• ISBN: 978-981-9775-14-9
• DOI: doi:10.1007/978-981-97-7514-9
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: Mishra, Abhishek: Special integrals. - Singapore : Springer Nature, 2025. - xvi, 382 Seiten
• K10plus-PPN: 192092602X
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

Binomial Series -- Trigonometrical Series -- Special Integrals -- Pseudo-Exponential Functions -- Series Sums using Special Integrals -- Solutions to Binomial Series -- Solutions to Trigonometrical Series.

Abstract

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.