Introduction to Hypergeometric, Supertrigonometric, and Superhyperbolic Functions

The book provides a basic introduction to hypergeometric, supertrigonometric, and superhyperbolic functions from the special functions viewpoint, highlighting their applications in describing complex behaviors in mathematics, physics, chemistry, and engineering.

Format: Paperback / softback
Length: 502 pages
Publication date: 28 January 2021
Publisher: Elsevier Science Publishing Co Inc

An Introduction to Hypergeometric, Supertigonometric, and Superhyperbolic Functions delves into the realm of newly established hypergeometric, supertrigonometric, and superhyperbolic functions, offering a foundational understanding from the perspective of special functions. These special functions, including the Euler Gamma function, Euler Beta function, Clausen hypergeometric series, and Gauss hypergeometric, have proven invaluable in describing complex behaviors that arise in mathematics, physics, chemistry, and engineering. By harnessing the power of these functions, researchers have been able to unravel the intricacies of real-world phenomena, providing insights into a wide range of scientific and technological applications.

The study of hypergeometric, supertrigonometric, and superhyperbolic functions has emerged as a vital area of research in recent years. These functions, which are extensions of classical trigonometric and hyperbolic functions, have found applications in diverse fields such as mathematics, physics, chemistry, and engineering. In this essay, we will provide an introduction to these functions, their properties, and their applications.

Hypergeometric functions are a class of special functions that arise from the study of geometric series. They are defined as the sum of a finite number of terms, each of which is a product of a fixed number of variables. Hypergeometric functions have a wide range of applications in mathematics, including number theory, combinatorics, and probability theory. For example, the hypergeometric function F_n(a, b; c) is used to calculate the number of ways to choose k items from a set of n items without repetition or order.

Supertigonometric functions are also a class of special functions that arise from the study of trigonometric functions. They are defined as the sum of a finite number of terms, each of which is a product of a variable and a complex number. Supertrigonometric functions have a wide range of applications in physics, including quantum mechanics, electromagnetism, and relativity. For example, the supertrigonometric function F_m(a, b; c) is used to calculate the probability of finding a particle in a specific region of space.

Superhyperbolic functions are a class of special functions that arise from the study of hyperbolic functions. They are defined as the sum of a finite number of terms, each of which is a product of a variable and a hyperbolic number. Superhyperbolic functions have a wide range of applications in mathematics, including number theory, differential equations, and geometric analysis. For example, the superhyperbolic function F_n(a, b; c) is used to calculate the number of solutions to a differential equation of the form

Weight: 1044g
Dimension: 211 x 262 x 30 (mm)
ISBN-13: 9780128241547