on a class of incomplete gamma functions with applications

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On A Class Of Incomplete Gamma Functions With Applications

Author : M. Aslam Chaudhry
ISBN : 9781420036046
Genre : Mathematics
File Size : 77. 38 MB
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The subject of special functions is rich and expanding continuously with the emergence of new problems encountered in engineering and applied science applications. The development of computational techniques and the rapid growth in computing power have increased the importance of the special functions and their formulae for analytic representations. However, problems remain, particularly in heat conduction, astrophysics, and probability theory, whose solutions seem to defy even the most general classes of special functions. On a Class of Incomplete Gamma Functions with Applications introduces a class of special functions, developed by the authors, useful in the analytic study of several heat conduction problems. It presents some basic properties of these functions, including their recurrence relations, special cases, asymptotic representations, and integral transform relationships. The authors explore applications of these generalized functions to problems in transient heat conduction, special cases of laser sources, and problems associated with heat transfer in human tissues. They also discuss applications to astrophysics, probability theory, and other problems in theory of functions and present a fundamental solution to time-dependent laser sources with convective-type boundary conditions. Appendices include an introduction to heat conduction, Fourier conduction, a table of Laplace transforms, and well-known results regarding the improper integrals. Filled with tabular and graphical representations for applications, this monograph offers a unique opportunity to add to your mathematical toolbox a new and useful class of special functions.

Mathematical Functions And Their Approximations

Author : Yudell L. Luke
ISBN : 9781483262451
Genre : Mathematics
File Size : 33. 72 MB
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Mathematical Functions and their Approximations is an updated version of the Applied Mathematics Series 55 Handbook based on the 1954 Conference on Mathematical Tables, held at Cambridge, Massachusetts. The aim of the conference is to determine the need for mathematical tables in view of the availability of high speed computing machinery. This work is composed of 14 chapters that cover the machinery for the expansion of the generalized hypergeometric function and other functions in infinite series of Jacobi and Chebyshev polynomials of the first kind. Numerical coefficients for Chebyshev expansions of the more common functions are tabulated. Other chapters contain polynomial and rational approximations for certain class of G-functions, the coefficients in the early polynomials of these rational approximations, and the Padé approximations for many of the elementary functions and the incomplete gamma functions. The remaining chapters describe the development of analytic approximations and expansions. This book will prove useful to mathematicians, advance mathematics students, and researchers.

Special Functions Their Applications

Author : N. N. Lebedev
ISBN : 9780486139890
Genre : Mathematics
File Size : 88. 42 MB
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Famous Russian work discusses the application of cylinder functions and spherical harmonics; gamma function; probability integral and related functions; Airy functions; hyper-geometric functions; more. Translated by Richard Silverman.

Theory And Application Of Special Functions

Author : Richard Askey
ISBN : 9781483216164
Genre : Mathematics
File Size : 37. 83 MB
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Theory and Application of Special Functions contains the proceedings of the Advanced Seminar on Special Functions sponsored by the Mathematics Research Center of the University of Wisconsin-Madison and held from March 31 to April 2, 1975. The seminar tackled the theory and application of special functions and covered topics ranging from the asymptotic estimation of special functions to association schemes and coding theory. Some interesting results, conjectures, and problems are given. Comprised of 13 chapters, this book begins with a survey of computational methods in special functions, followed by a discussion on unsolved problems in the asymptotic estimation of special functions. The reader is then introduced to periodic Bernoulli numbers, summation formulas, and applications; problems and prospects for basic hypergeometric functions; and linear growth models with many types and multidimensional Hahn polynomials. Subsequent chapters explore two-variable analogues of the classical orthogonal polynomials; special functions of matrix and single argument in statistics; and some properties of the determinants of orthogonal polynomials. This monograph is intended primarily for students and practitioners of mathematics.

Nist Handbook Of Mathematical Functions

Author : Frank W. J. Olver
ISBN : 9780521192255
Genre : Mathematics
File Size : 49. 74 MB
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The new standard reference on mathematical functions, replacing the classic but outdated handbook from Abramowitz and Stegun. Includes PDF version.

A Treatise On Generating Functions

Author : H. M. Srivastava
ISBN : 0470200103
Genre : Mathematics
File Size : 82. 91 MB
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Special Functions For Scientists And Engineers

Author : W. W. Bell
ISBN : 9780486317564
Genre : Technology & Engineering
File Size : 89. 23 MB
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Physics, chemistry, and engineering undergraduates will benefit from this straightforward guide to special functions. Its topics possess wide applications in quantum mechanics, electrical engineering, and many other fields. 1968 edition. Includes 25 figures.

Special Functions Of Mathematics For Engineers

Author : Larry C. Andrews
ISBN : 0819426164
Genre : Mathematics
File Size : 32. 12 MB
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Designed to serve as a classroom text for higher mathematical functions and a reference text for engineers and scientists, presents applications from such fields as statics, dynamics, statistical communication theory, fiber optics, heat conduction in solids, hybridation phenomena, and fluid mechanic

Special Functions

Author : Nico M. Temme
ISBN : 9781118030813
Genre : Mathematics
File Size : 43. 29 MB
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This book gives an introduction to the classical, well-known special functions which play a role in mathematical physics, especially in boundary value problems. Calculus and complex function theory form the basis of the book and numerous formulas are given. Particular attention is given to asymptomatic and numerical aspects of special functions, with numerous references to recent literature provided.

Computational Probability Applications

Author : Andrew G. Glen
ISBN : 9783319433172
Genre : Business & Economics
File Size : 80. 81 MB
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This focuses on the developing field of building probability models with the power of symbolic algebra systems. The book combines the uses of symbolic algebra with probabilistic/stochastic application and highlights the applications in a variety of contexts. The research explored in each chapter is unified by the use of A Probability Programming Language (APPL) to achieve the modeling objectives. APPL, as a research tool, enables a probabilist or statistician the ability to explore new ideas, methods, and models. Furthermore, as an open-source language, it sets the foundation for future algorithms to augment the original code. Computational Probability Applications is comprised of fifteen chapters, each presenting a specific application of computational probability using the APPL modeling and computer language. The chapter topics include using inverse gamma as a survival distribution, linear approximations of probability density functions, and also moment-ratio diagrams for univariate distributions. These works highlight interesting examples, often done by undergraduate students and graduate students that can serve as templates for future work. In addition, this book should appeal to researchers and practitioners in a range of fields including probability, statistics, engineering, finance, neuroscience, and economics.

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