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On a Class of Incomplete Gamma Functions with Applications by M. Aslam Chaudhry, Syed M. Zubair



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On a Class of Incomplete Gamma Functions with Applications written by M. Aslam Chaudhry, Syed M. Zubair.
Engineering and physics applications demand a thorough knowledge of applied mathematics and a good understand of special functions. These functions commonly arise in such areas of applications as head conduction, communication systems, electro-optics, approximation theory, probaility theory and electric circuit theory, among others. The subjectspecial functions is quite rich an expanding continously with the emergence of new problems in the areas of applications in engineering and applied sciences. The solutions of a large body of problems are expressible in terms of some special cases of the mot general class of the Meijer G-functions and the Fox H-functions. The association of hypergeometric functions of several variables and their q-extenstions with the funtions arising in theoretical statistics, applied mathematics adn engineering problems seems to be well estabised. The continuous developement in partition theory, combinatorics, astronomy, and others has led to the discovery of new 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.

On a Class of Incomplete Gamma Functions with Applications written by M. Aslam Chaudhry, Syed M. Zubair cover the following topics.


  • 1. Generalized Gamma Fuction
    2. The Generalized Incomlete Gamma Fuction
    3. The family of the Gamma Functions
    4. Extension of Generalized Incomplete Gamma Functions
    5. Extended Beta Function
    6. Extended Incomplete Beta Function
    7. Extended Riemann Zeta Function
    8. Phase Change Heat Transfer
    9. Transient Heat Conduction Problems
    10. Heat Conduction Due to Laser Sources
    11. Unified Approach to Heat Source Problems
    Appendices
    A. Heat Conduction
    B. Table of Laplace Transforms
    C. Integrals Dependent on Parameters
    Refrences
    Symbols and Abbreviations
    Index

  • Publisher: CRC Press,
    Year: 2002,
    ISBN: 1584881437,9781584881438,9781420036046

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