Some fractional-calculus results for the H̄-function associated with a class of Feynman integrals

Russian Journal of Mathematical Physics

Volumn 13, Issue 1, 2006, Pages 94-100

  Srivastava, H M ^a   Lin, Shy Der ^b   Wang, Pin Yu ^c  

^a UNIVERSITY OF VICTORIA   (Canada)

^b CHUNG YUAN CHRISTIAN UNIVERSITY   (Taiwan)

^c NANYA INSTITUTE OF TECHNOLOGY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33845355798     PISSN: 10619208     EISSN: None     Source Type: Journal    
DOI: 10.1134/S1061920806010092     Document Type: Article

References (31)

1. R. G. Buschman and H. M. Srivastava, "The H̄ Function Associated with a Certain Class of Feynman Integrals," J. Phys. A: Math. Gen. 23, 4707-4710 (1990).
2. C. M. Carracedo and M. S. Alix, The Theory of Fractional Powers of Operators, North-Holland Mathematical Studies 187 (Elsevier (North-Holland) Science Publishers, Amsterdam, 2001).
3. T. Craven and G. Csordas, "The Fox-Wright Functions and Laguerre Multiplier Sequences," J. Math. Anal. Appl. 314, 109-125 (2006).
4. M. R. Dotsenko, "On Some Applications of Wright's Hypergeometric Function," C. R. Acad. Bulgare Sci. 44 (6), 13-16 (1991).
5. A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions, Vol. I (McGraw-Hill Book Company, New York, 1953).
6. A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Tables of Integral Transforms, Vol. II (McGraw-Hill Book Company, New York, 1954).
7. C. Fox, "The Asymptotic Expansion of Generalized Hypergeometric Functions," Proc. London Math. Soc. Ser. 2 27, 389-400 (1928).
8. C. Fox, "The G and H Functions as Symmetrical Fourier Kernels," Trans. Amer. Math. Soc. 98, 395-429 (1961).
9. L. Galué, "Differintegrals of Wright's Generalized Hypergeometric Function," Internat. J. Appl. Math. 10, 255-267 (2002).
10. R. Hilfer (Editor), Applications of Fractional Calculus in Physics (World Scientific Publishing Company, Singapore, 2000).
11. A. A. Inayat-Hussain, "New Properties of Hypergeometric Series Derivable from Feynman Integrals. I: Transformation and Reduction Formulae," J. Phys. A: Math. Gen. 20, 4109-4117 (1987).
12. A. A. Inayat-Hussain, "New Properties of Hypergeometric Series Derivable from Feynman Integrals. II: A Generalization of the H Function," J. Phys. A: Math. Gen. 20, 4119-4128 (1987).
13. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematical Studies 204 (Elsevier (North-Holland) Science Publishers, Amsterdam, 2006).
14. V. Kiryakova, Generalized Fractional Calculus and Applications, Pitman Research Notes in Mathematics 301 (Longman Scientific and Technical, Harlow, 1994).
15. V. Kiryakova, "All the Special Functions Are Fractional Differintegrals of Elementary Functions," J. Phys. A: Math. Gen. 30, 5085-5103 (1997).
16. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, A Wiley-Interscience Publication (John Wiley and Sons, New York, 1993).
17. K. Nishimoto, Fractional Calculus, Vols. I-V (Descartes Press, Koriyama, 1984, 1987, 1989, 1991, 1996).
18. K. Nishimoto, An Essence of Nishimoto's Fractional Calculus (Calculus of the 21st Century): Integrations and Differentiations of Arbitrary Order (Descartes Press, Koriyama, 1991).
19. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing, Wiley Series in Pure and Applied Optics (John Wiley and Sons, New York, 2000).
20. I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Mathematics in Science and Engineering 198 (Academic Press, New York, 1999).
21. S. Salinas de Romero, A. Prieto, and K. Nishimoto, "N-Fractional Differintegral of Generalized Hypergeometric Function," J. Fract. Calc. 15, 55-60 (1999).
22. S. G. Samko, A. A. Kilbas and O. I. Marichev, Integrals and Derivatives of Fractional Order and Some of Their Applications (Nauka i Tekhnika, Minsk, 1987);
23. translated in Fractional Integrals and Derivatives: Theory and Applications (Gordon and Breach Science Publishers, Reading, 1993).
24. H. M. Srivastava and R. G. Buschman, Theory and Applications of Convolution Integral Equations, Kluwer Series on Mathematics and Its Applications 79 (Kluwer Academic Publishers, Dordrecht, 1992).
25. H. M. Srivastava, K. C. Gupta, and S. P. Goyal, The H-Functions of One and Two Variables with Applications (South Asian Publishers, New Delhi and Madras, 1982).
26. H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series (Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, 1985).
27. H. M. Srivastava, S. Owa, and K. Nishimoto, "Some Fractional Differintegral Equations," J. Math. Anal. Appl. 106, 360-366 (1985).
28. G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed. (Cambridge University Press, Cambridge, 1944).
29. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; with an Account of the Principal Transcendental Functions, 4th ed. (Cambridge University Press, Cambridge, 1927).
30. E. M. Wright, "The Asymptotic Expansion of the Generalized Hypergeometric Function," J. London Math. Soc. 10, 286-293 (1935).
31. E. M. Wright, "The Asymptotic Expansion of the Generalized Hypergeometric Function," Proc. London Math. Soc. Ser. 2 46, 389-408 (1940).