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An Introduction to Hypergeometric, Supertrigonometric, and Superhyperbolic Functions

1st Edition - January 23, 2021

Author: Xiao-Jun Yang

Paperback ISBN:

9 7 8 - 0 - 1 2 - 8 2 4 1 5 4 - 7

eBook ISBN:

9 7 8 - 0 - 3 2 3 - 8 5 2 8 2 - 1

An Introduction to Hypergeometric, Supertigonometric, and Superhyperbolic Functions gives a basic introduction to the newly established hypergeometric, supertrigonometric, and… Read more

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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.

1 Euler Gamma function, Pochhammer symbols and Euler beta function1.1 The Euler gamma function1.2 Pochhammer symbols1.3 Euler beta function

2 Hypergeometric supertrigonometric and superhyperbolic functions via Clausen hypergeometricseries2.1 Definitions, convergences, and properties for the Clausen hypergeometric series2.2 The hypergeometric supertrigonometric functions of the Clausen hypergeometric series2.3 The hypergeometric superhyperbolic functions for the Clausen hypergeometric series.2.4 The hypergeometric supertrigonometric functions with three numerator parameters and twodenominator parameters2.5 The hypergeometric superhyperbolic functions with three numerator parameters and two denominatorparameters2.6 The analytic number theory involving the Clausen hypergeometric functions

3 Hypergeometric supertrigonometric and superhyperbolic functions via Gauss hypergeometricseries3.1 Definitions, convergences, and properties for the Gauss hypergeometric series3.2 The hypergeometric supertrigonometric functions of the Gauss hypergeometric series3.3 The hypergeometric superhyperbolic functions for the Gauss hypergeometric series3.4 The analytic number theory involving the Gauss hypergeometric functions

4 Hypergeometric supertrigonometric and superhyperbolic functions via Kummer confluenthypergeometric series4.1 The Kummer confluent hypergeometric series of first type4.2 The hypergeometric supertrigonometric functions of the Kummer confluent hypergeometric series offirst stype4.3 The hypergeometric superhyperbolic functions of the Kummer confluent hypergeometric series of firststype4.4 The Kummer confluent hypergeometric series of second type4.5 The hypergeometric supertrigonometric functions of the Kummer confluent hypergeometric series ofsecond type4.6 The hypergeometric superhyperbolic functions of the Kummer confluent hypergeometric series ofsecond stype4.7 The analytic number theory involving the Kummer confluent hypergeometric series

5 Hypergeometric supertrigonometric and superhyperbolic functions via Jacobi polynomials5.1 Definition, properties and theorems for the Jacobi polynomials5.2 Hypergeometric supertrigonometric functions for the Jacobi polynomials5.3 Hypergeometric superhyperbolic functions for the Jacobi polynomials5.4 Definition, properties and theorems for the Jacobi-Luke type polynomials5.5 Hypergeometric supertrigonometric functions for the Jacobi-Luke type polynomials5.6 Hypergeometric superhyperbolic functions for the Jacobi-Luke type polynomialsand superhyperbolic functions

6 Hypergeometric supertrigonometric functions and superhyperbolic functions via Laguerrepolynomials6.1 Definition, properties and theorems for the Laguerre polynomials6.2 The hypergeometric supertrigonometric functions of the Laguerre polynomials6.3The hypergeometric superhyperbolic functions of the Laguerre polynomials6.4 Extended works containing the Laguerre polynomials6.5 Supertrigonometric functions containing the Laguerre polynomials6.6 Hypergeometric superhyperbolic functions containing the Laguerre polynomials6.7 Hypergeometric supertrigonometric functions for the Szeg function6.8 Hypergeometric superhyperbolic functions for the Szeg function6.9 Hypergeometric supertrigonometric functions for the Chaundy function6.10 Hypergeometric superhyperbolic functions for the Chaundy function

7 Hypergeometric supertrigonometric and superhyperbolic functions via Legendre Polynomials7.1 Definition, properties and theorems for the Legendre Polynomials7.2 The hypergeometric supertrigonometric functions of the Legendre Polynomials7.3 The hypergeometric superhyperbolic functions of the Legendre Polynomials7.4 Hypergeometric supertrigonometric for the Legendre type polynomials7.5 Hypergeometric superhyperbolic functions for the Legendre type polynomials