An Introduction to Hypergeometric, Supertrigonometric, and Superhyperbolic Functions

An Introduction to Hypergeometric, Supertrigonometric, and Superhyperbolic Functions

1st Edition - January 23, 2021

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  • Author: Xiao-Jun Yang
  • Paperback ISBN: 9780128241547
  • eBook ISBN: 9780323852821

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Description

An Introduction to Hypergeometric, Supertigonometric, and Superhyperbolic Functions gives a basic introduction to the newly established hypergeometric, supertrigonometric, and superhyperbolic functions from the special functions viewpoint. The special functions, such as the Euler Gamma function, the Euler Beta function, the Clausen hypergeometric series, and the Gauss hypergeometric have been successfully applied to describe the real-world phenomena that involve complex behaviors arising in mathematics, physics, chemistry, and engineering.

Key Features

  • Provides a historical overview for a family of the special polynomials
  • Presents a logical investigation of a family of the hypergeometric series
  • Proposes a new family of the hypergeometric supertrigonometric functions
  • Presents a new family of the hypergeometric superhyperbolic functions

Readership

Researchers in the fields of mathematics, physics, chemistry and engineering. It can also be used as a textbook for an introductory course on special functions and applications for senior undergraduate and graduate students in the above- mentioned areas. Research scientists and students in the fields of Applied Mathematics, Pure Mathematics, Mathematical Analysis, Special Functions

Table of Contents

  • 1 Euler Gamma function, Pochhammer symbols and Euler beta function
    1.1 The Euler gamma function
    1.2 Pochhammer symbols
    1.3 Euler beta function

    2 Hypergeometric supertrigonometric and superhyperbolic functions via Clausen hypergeometric
    series
    2.1 Definitions, convergences, and properties for the Clausen hypergeometric series
    2.2 The hypergeometric supertrigonometric functions of the Clausen hypergeometric series
    2.3 The hypergeometric superhyperbolic functions for the Clausen hypergeometric series.
    2.4 The hypergeometric supertrigonometric functions with three numerator parameters and two
    denominator parameters
    2.5 The hypergeometric superhyperbolic functions with three numerator parameters and two denominator
    parameters
    2.6 The analytic number theory involving the Clausen hypergeometric functions

    3 Hypergeometric supertrigonometric and superhyperbolic functions via Gauss hypergeometric
    series
    3.1 Definitions, convergences, and properties for the Gauss hypergeometric series
    3.2 The hypergeometric supertrigonometric functions of the Gauss hypergeometric series
    3.3 The hypergeometric superhyperbolic functions for the Gauss hypergeometric series
    3.4 The analytic number theory involving the Gauss hypergeometric functions

    4 Hypergeometric supertrigonometric and superhyperbolic functions via Kummer confluent
    hypergeometric series
    4.1 The Kummer confluent hypergeometric series of first type
    4.2 The hypergeometric supertrigonometric functions of the Kummer confluent hypergeometric series of
    first stype
    4.3 The hypergeometric superhyperbolic functions of the Kummer confluent hypergeometric series of first
    stype
    4.4 The Kummer confluent hypergeometric series of second type
    4.5 The hypergeometric supertrigonometric functions of the Kummer confluent hypergeometric series of
    second type
    4.6 The hypergeometric superhyperbolic functions of the Kummer confluent hypergeometric series of
    second stype
    4.7 The analytic number theory involving the Kummer confluent hypergeometric series

    5 Hypergeometric supertrigonometric and superhyperbolic functions via Jacobi polynomials
    5.1 Definition, properties and theorems for the Jacobi polynomials
    5.2 Hypergeometric supertrigonometric functions for the Jacobi polynomials
    5.3 Hypergeometric superhyperbolic functions for the Jacobi polynomials
    5.4 Definition, properties and theorems for the Jacobi-Luke type polynomials
    5.5 Hypergeometric supertrigonometric functions for the Jacobi-Luke type polynomials
    5.6 Hypergeometric superhyperbolic functions for the Jacobi-Luke type polynomials
    and superhyperbolic functions

    6 Hypergeometric supertrigonometric functions and superhyperbolic functions via Laguerre
    polynomials
    6.1 Definition, properties and theorems for the Laguerre polynomials
    6.2 The hypergeometric supertrigonometric functions of the Laguerre polynomials
    6.3The hypergeometric superhyperbolic functions of the Laguerre polynomials
    6.4 Extended works containing the Laguerre polynomials
    6.5 Supertrigonometric functions containing the Laguerre polynomials
    6.6 Hypergeometric superhyperbolic functions containing the Laguerre polynomials
    6.7 Hypergeometric supertrigonometric functions for the Szeg function
    6.8 Hypergeometric superhyperbolic functions for the Szeg function
    6.9 Hypergeometric supertrigonometric functions for the Chaundy function
    6.10 Hypergeometric superhyperbolic functions for the Chaundy function

    7 Hypergeometric supertrigonometric and superhyperbolic functions via Legendre Polynomials
    7.1 Definition, properties and theorems for the Legendre Polynomials
    7.2 The hypergeometric supertrigonometric functions of the Legendre Polynomials
    7.3 The hypergeometric superhyperbolic functions of the Legendre Polynomials
    7.4 Hypergeometric supertrigonometric for the Legendre type polynomials
    7.5 Hypergeometric superhyperbolic functions for the Legendre type polynomials

Product details

  • No. of pages: 502
  • Language: English
  • Copyright: © Academic Press 2021
  • Published: January 23, 2021
  • Imprint: Academic Press
  • Paperback ISBN: 9780128241547
  • eBook ISBN: 9780323852821

About the Author

Xiao-Jun Yang

Xiao-Jun Yang
Dr. Xiao-Jun Yang is a full professor of China University of Mining and Technology, China. He was awarded the 2019 Obada-Prize, the Young Scientist Prize (Turkey), and Springer's Distinguished Researcher Award. His scientific interests include: Viscoelasticity, Mathematical Physics, Fractional Calculus and Applications, Fractals, Analytic Number Theory, and Special Functions. He has published over 160 journal articles and 4 monographs, 1 edited volume, and 10 chapters. He is currently an editor of several scientific journals, such as Fractals, Applied Numerical Mathematics, Mathematical Methods in the Applied Sciences, Mathematical Modelling and Analysis, Journal of Thermal Stresses, and Thermal Science, and an associate editor of Journal of Thermal Analysis and Calorimetry, Alexandria Engineering Journal, and IEEE Access.

Affiliations and Expertise

Full Professor, China University of Mining and Technology, Xuzhou, China

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  • Purnima Wed Apr 27 2022

    An Introduction to Hypergeometric, Supertrigonometric, and Superhyperbolic Functions

    Nice book for further research in hypergeometric function