Extended hypergeometric and confluent hypergeometric functions

Applied Mathematics and Computation

Volumn 159, Issue 2, 2004, Pages 589-602

  Chaudhry, M Aslam ^a   Qadir, Asghar ^b   Srivastava, H M ^c   Paris, R B ^d  

^a KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS   (Saudi Arabia)

^b QUAID I AZAM UNIVERSITY   (Pakistan)

^c UNIVERSITY OF VICTORIA   (Canada)

^d UNIVERSITY OF ABERTAY DUNDEE   (United Kingdom)

Author keywords

Asymptotic behavior; Extended beta function; Generalized gamma function; Hypergeometric and confluent hypergeometric functions; Kummer's first formula; Recurrence relations

Indexed keywords

COMPUTATIONAL GEOMETRY; DIFFERENCE EQUATIONS; INTEGRATION; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; PARAMETER ESTIMATION; POLYNOMIALS;

ASYMPTOTIC BEHAVIOR; EXTENDED BETA FUNCTION; GENERALIZED GAMMA FUNCTION; HYPERGEOMETRIC EQUATIONS;

FUNCTIONS;

EID: 5644282901     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2003.09.017     Document Type: Article

References (15)

1. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Washington, DC, 1964, Reprinted by Dover Publications, New York, 1970.
2. Andrews G.E., Askey R., Roy R. Special Functions. 1999;Cambridge University Press, Cambridge.
3. Chaudhry M.A., Temme N.M., Veling E.J.M. Asymptotic and closed form of a generalized incomplete gamma function. J. Comput. Appl. Math. 67:1996;371-379.
4. Chaudhry M.A., Qadir A., Rafique M., Zubair S.M. Extension of Euler's beta function. J. Comput. Appl. Math. 78:1997;19-32.
5. Chaudhry M.A., Zubair S.M. Generalized incomplete gamma functions with applications. J. Comput. Appl. Math. 55:1994;99-124.
6. Chaudhry M.A., Zubair S.M. On a Class of Incomplete Gamma Functions with Applications. 2002;CRC Press (Chapman and Hall), Boca Raton, FL.
7. Davis P.J. Leonhard Euler's integral: a historical profile of the gamma function. Amer. Math. Monthly. 66:1959;849-869.
8. Erdélyi A., Magnus W., Oberhettinger F., Tricomi F.G. Higher Transcendental Functions, vol. I. 1953;McGraw-Hill, New York.
9. Erdélyi A., Magnus W., Oberhettinger F., Tricomi F.G. Tables of Integral Transforms, vol. I. 1954;McGraw-Hill, New York.
10. I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products, (Corrected and Enlarged Ed. prepared by A. Jeffrey and D. Zwillinger), Sixth Ed., Academic Press, New York, 2000.
11. Miller A.R. Reduction of a generalized incomplete gamma function, related Kampé de Fériet functions, and incomplete Weber integrals. Rocky Mountain J. Math. 30:2000;703-714.
12. E.D. Rainville, Special Functions, Macmillan Company, New York, 1960; Reprinted by Chelsea Publishing Company, Bronx, New York, 1971.
13. Slater L.J. Generalized Hypergeometric Functions. 1966;Cambridge University Press, Cambridge.
14. Srivastava H.M., Karlsson P.W. Multiple Gaussian Hypergeometric Series. 1985;Halsted Press (John Wiley and Sons), New York.
15. Temme N.M. Special Functions: An Introduction to the Classical Functions of Mathematical Physics. 1996;John Wiley and Sons, New York.