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Goĭ, T. P.

Special functions generated by rising and central factorial powers. (Russian. English summary) Zbl 07606830

Vestn. Tomsk. Gos. Univ., Mat. Mekh. 2016, No. 2(40), 19-32 (2016).

MSC:

33-XX Special functions
34-XX Ordinary differential equations

Keywords:

rising factorial power; central factorial power; Fresnel integrals; generalized hypergeometric function; Cauchy problem
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Full Text: DOI MNR

References:

[1] Goy T. P., Zatorsky R. A., “New functions generated by rising factorial powers and their properties”, Bukovyna Math. Journal, 1:1-2 (2013), 28-33 (In Ukrainian) · Zbl 1391.33008
[2] Goy T. P., “Non-elementary functions generated by central factorial powers”, Bulletin of V. N. Karazin Kharkiv National University. Series: Mathematics, Applied Mathematics and Mechanics, 2014, no. 1133, 131-139 (In Ukrainian) · Zbl 1324.33016
[3] Goy T. P., “On central factorial powers and some of their applications”, Mathematics and mathematical education. Theory and practice, 9, YSTU, Yaroslavl, 2014, 30-35
[4] Goy T. P., Zatorsky R. A., “New integral functions generated by rising factorial powers”, Carpathian Math. Publ., 5:2 (2013), 217-224 · Zbl 1391.33008 · doi:10.15330/cmp.5.2.217-224
[5] Goy T. P., Zatorsky R. A., “On a nonelementary function of the Dawson”s integral type”, Bulletin of Taras Shevchenko Kyiv National University. Series: Physics and Mathematics, 2014, no. 1, 15-19
[6] Goy T. P., “Integrals of functions generated by rising factorial powers”, Taurida Journal of Computer Science and Mathematics, 24:1 (2014), 14-22 (in Ukrainian)
[7] Goy T. P., “New functions defined by factorial powers”, Mathematical and Computer Modelling. Series: Physical and mathematical sciences, 2014, no. 11, 18-29 (in Ukrainian)
[8] Goy T. P., “On differential equations of functions defined by rising and central factorials”, Modern Problems of the Analysis of Dynamic Systems. Appendices in Equipment Technologies, Proc. Intern. Conf., v. 1, VSFA, Voronezh, 2014, 58-61 · doi:10.12737/4702
[9] Jordan C., Calculus of Finite Differences, Chelsea Publishing, N.Y., 1939 · Zbl 0060.12309
[10] Steffensen J. F., “On the definition of the central factorial”, J. Inst. Actuaries, 64:2 (1933), 165-168 · Zbl 0007.22004
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[12] Zatorsky R. A., Malarchuk A. R., “Factorial powers and triangular matrices”, Carpathian Math. Publ., 1:2 (2009), 161-171 (In Ukrainian) · Zbl 1391.15027
[13] Comtet L., Advanced Combinatorics: The Art of Finite and Infinite Expansions, D. Reider Publishing, 1974 · Zbl 0283.05001
[14] Roman S., The Umbral Calculus, Academic Press, 1984 · Zbl 0536.33001
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[16] Bateman H., Erdelyi A., Higher Transcendental Functions, v. 1, McGraw-Hill, 1953 · Zbl 0143.29202
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