On a Class of Incomplete Gamma Functions with Applications
Seiten
2001
Chapman & Hall/CRC (Verlag)
978-1-58488-143-8 (ISBN)
Chapman & Hall/CRC (Verlag)
978-1-58488-143-8 (ISBN)
The closed-form solutions to a considerable number of problems in applied mathematics and engineering can be expressed in terms of incomplete Gamma functions. Focusing on various heat conduction problems, this title provides a comprehensive study of these functions. It describes the properties of the class of generalized Gamma functions.
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.
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.
Syed M. Zubair, M. Aslam Chaudhry
Generalized Gamma Function. The Generalized Incomplete Gamma Functions. The Family of Gamma Functions. Extension of Generalized Incomplete Gamma Functions. Extended Beta Function. Extended Incomplete Gamma Functions. Extended Riemann Zeta Functions. Phase-Change Heat-Transfer. Heat Conduction due to Time-Dependent Laser Sources. A Unified Approach to Heat Source Problems. Appendices. References. Symbols. Index.
| Erscheint lt. Verlag | 21.8.2001 |
|---|---|
| Zusatzinfo | 66 Tables, black and white |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 850 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| ISBN-10 | 1-58488-143-7 / 1584881437 |
| ISBN-13 | 978-1-58488-143-8 / 9781584881438 |
| Zustand | Neuware |
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