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Reduction formulas for Kampé de Fériet functions associated with certain classes of incomplete Lipschitz-Hankel type integrals of cylindrical functions. (English) Zbl 0737.33002

See the preview in Zbl 0723.33005.

MSC:

33C20 Generalized hypergeometric series, \({}_pF_q\)
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)

Citations:

Zbl 0723.33005
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Full Text: DOI

References:

[1] Miller, A. R., A note on incomplete integrals of cylindrical functions, J. Franklin Inst., Vol. 326, 571-577 (1989) · Zbl 0683.33006
[2] Agrest, M. M.; Maksimov, M. S., Theory of Incomplete Cylindrical Functions and Their Applications (1971), Springer: Springer New York · Zbl 0215.43401
[3] Miller, A. R., Reduction formulae for Kampé de Fériet functions \(F^{p:2;1}_{q\):1;0 · Zbl 0719.33007
[4] Srivastava, H. M., Reduction and summation formulae for certain classes of generalized multiple hypergeometric series arising in physical and quantum chemical applications, J. Phys. A : Math. Gen., Vol. 18, 3079-3085 (1985) · Zbl 0556.33003
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[9] Rainville, E. D., Special Functions (1960), Macmillan: Macmillan New York · Zbl 0050.07401
[10] Rainville, E. D., Special Functions (1971), Chelsea: Chelsea New York · Zbl 0050.07401
[11] Miller, A. R.; Moskowitz, I. S., Incomplete Weber integrals of cylindrical functions, J. Franklin Inst., Vol. 328, 445-458 (1991) · Zbl 0736.33011
[12] Exton, H., Handbook of Hypergeometric Integrals (1978), Wiley/Halsted: Wiley/Halsted New York · Zbl 0377.33001
[13] Luke, Y. L., Integrals of Bessel Functions (1962), McGraw-Hill: McGraw-Hill New York · Zbl 0144.06902
[14] Prudnikov, A. P.; Brychkov, Yu. A.; Marichev, I. O., Integrals and Series, Vol. 2 (1986), Gordon and Breach: Gordon and Breach New York · Zbl 0606.33001
[15] Watson, G. N., A Treatise on the Theory of Bessel Functions (1944), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0063.08184
[16] Abramowitz, M.; Stegun, I. A., Handbook of Mathematical FDunctions with Formulas, Graphs, and Mathematical Tables (1964), National Bureau of Standards: National Bureau of Standards Washington, DC · Zbl 0171.38503
[17] Abramowitz, M.; Stegun, I. A., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (1965), Dover: Dover New York · Zbl 0515.33001
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