On a class of incomplete gamma functions with applications. (©2002)

• Record Type: Book
• Further Information: Note: M. Aslam Chaudhry, Syed M. Zubair.
• Other Names: Chaudhry, M. Aslam; Zubair, Syed M
• Contents: GENERALIZED GAMMA FUNCTION; The Gamma Fun ction G(a); Definition of the Generalized Gamma Function; Properties of the Generalized Gamma Function; Mellin and Laplace Transforms; Asymptotic Representations; The Macdonald Function; The Digamma Function y(x); Generalization of Psi (Digamma) Function; Integral Representations of yb (a); Properties of the Generalized Psi Function; Graphical and Tabular Representations; THE GENERALIZED INCOMPLETE GAMMA FUNCTIONS; The Incomplete Gamma Functions; Definition of the Generalized Incomplete Gamma Functions; Properties of the Incomplete Generalized Gamma Functions; Convolution Representations and Laplace Transforms; Connection with Other Special Functions; KdF Functions and Incomplete Integrals; Representation in terms of KdF Functions; Reduction Formulas for F0:2;1 2:0;0[x, y]; Integrals of Product of Bessel and Gamma Functions; Asymptotic Representations; Integral Representation for G(a, x;b); Graphical and Tabular Representations; THE FAMILY OF THE GAMMA FUNCTIONS; The Family of Incomplete Gamma Functions; The Generalized Error Functions; The Generalized Exponential Integral function; The Generalized Fresnel Integrals; The Decomposition Functions; The Extended Decomposition functions; The E(u, v) and F(u, v) Functions; The e(u) and f(u) Functions; Graphical and Tabular Representations; EXTENSION OF GENERALIZED INCOMPLETE GAMMA FUNCTIONS; Introduction; The Decomposition Formula; Recurrence Relations; Laplace and K-Transform Representation; Parametric Differentiation and Integration; Connection with Other Special Functions; Integral Representations; Differential Representations; The Mellin Transform Representation; EXTENDED BETA FUNCTION; The Beta Function; The Incomplete Beta Function; The Beta Probability Distribution; Definition of the Extended Beta Function; Properties of the Extended Beta Function; Integral Representations of the Extended Beta Function; Conncection with Other Special Functions; Representations in Terms of Whittaker functions; Extended Incomplete Beta Function; The Extended Beta Distribution; Graphical and Tabular Representations; EXTENDED INCOMPLETE GAMMA FUNCTIONS; Introduction; Definition of the Extended Incomplete Gamma Functions; The Decomposition Formula; Recurrence Formula; Connection with Other Special Functions; The H-Function; Incomplete Fox H-Functions; EXTENDED RIEMANN ZETA FUNCTIONS; Introduction; Bernoulli's Numbers and Polynomials; The Zeta Function; Zeros of the Zeta Function and the Function p(x); The Extended Zeta Function z(a); The Second Extended Zeta Function zb*(a); The Hurwitz Zeta Function; Extended Hurwitz Zeta Functions; Extended Hurwitz Formulae; Further Remarks and Comments; Graphical and Tabular Representations; PHASE-CHANGE HEAT-TRANSFER; Introduction; Constant Temperature Boundary Conditions; Convective Boundary Conditions; Freezing of Tissues around a Capillary Tube; Freezing of Binary Alloys; Freezing Around an Impurity; Numerical Methods for Phase-Change Problems; HEAT CONDUCTION WITH TIME-DEPENDENT BOUNDARY CONDITIONS; Introduction; Time-Dependent Surface Temperatures; Time-Dependent Surface Heat Fluxes; Illustrative Example; HEAT CONDUCTION DUE TO TIME-DEPENDENT LASER SOURCES; Introduction; Mathematical Formulation; Some Cases of Practical Interest; A UNIFIED APPROACH TO HEAT SOURCE PROBLEMS; Introduction; Thermal Explosions; Continuously Operating Heat Sources; APPENDICES; Heat Conduction; Table of Laplace Transforms; Integrals Dependent of Parameters; REFERENCES; SYMBOLS; INDEX
• Publisher Details: Boca Raton : CRC Press
• Publication Date: 2002
• Copyright Date: 2002
• Extent: 1 online resource (xi, 493 pages), illustrations
• Subjects: 515/.52; Gamma functions; MATHEMATICS -- Calculus; MATHEMATICS -- Mathematical Analysis; Gamma functions; Electronic books
• Languages: English
• ISBNs: 1584881437; 9781584881438; 1420036041; 9781420036046
• Notes: Note: Includes bibliographical references and index.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.