Innovative Integrals and Their Applications I

The book develops integral identities involving multidimensional functions and infinite limits of integration, using the multivariate power substitution and its variants, and permutation symmetry. It works best when applied to integrals with certain characteristics, leading to new and useful results. Results include the gamma function, hypergeometric functions, complementary error function, exponential integral function, and Riemann zeta function. The intended audience is junior and senior sciences majors, graduate students, and junior and established researchers.

Format: Hardback
Length: 319 pages
Publication date: 15 November 2022
Publisher: Springer International Publishing AG

This book delves into the development of integral identities, primarily involving multidimensional functions and infinite limits of integration, which pose significant challenges when evaluated using conventional methods. It presents a methodology rooted in the multivariate power substitution and its variations, aided by the powerful software tool Mathematica. The approaches introduced encompass the generalized method of exhaustion, the multivariate power substitution, and the utilization of permutation symmetry to evaluate definite integrals, which hold immense importance in their own right and serve as crucial intermediate steps toward more intricate computations. A fundamental principle underlying these methods is that they yield the most favorable results when applied to integrals possessing specific characteristics as a starting point. While the majority of integrals, when used as a starting point, may result in either no solution or a well-known outcome, there exists a unique class of integrals known as innovative integrals. When these innovative integrals serve as the initial basis for these approaches, they can lead to the discovery of novel and valuable results, as well as empower the reader to generate numerous other new results that are not explicitly covered in the book.

The reader will encounter a diverse array of innovative techniques for evaluating integrals, with a strong emphasis on leveraging tools like Mathematica to obtain practical and previously unknown results. The presented results encompass a wide range of mathematical functions, including the gamma function, hypergeometric functions, complementary error function, exponential integral function, and the Riemann zeta function, which will be introduced as they arise throughout the text.

The book concludes with a selection of engineering applications, showcasing the practical relevance of the discussed integral identities. These applications span various fields, such as wave propagation, antenna theory, non-Gaussian and weighted Gaussian distributions, and other areas. The intended audience for this book includes junior and senior sciences majors who are considering pursuing further studies in mathematics or related fields.

Weight: 664g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031178702
Edition number: 1st ed. 2022