Note on the Degenerate Gamma Function

T. Kim; D. S. Kim

doi:10.1134/s1061920820030061

journal article Jul 01, 2020

Note on the Degenerate Gamma Function

T. Kim

D. S. Kim

Russian Journal of Mathematical Physics Vol. 27 No. 3 pp. 352-358 · Pleiades Publishing Ltd

View at Publisher Save 10.1134/s1061920820030061

Topics

No keywords indexed for this article. Browse by subject →

References

22

[1]

C. Adiga, “A Note on the $$q$$-Gamma and $$q$$-Beta Functions,” Math. Balkanica, 9, 35–41 (1995).

[2]

T. H. Gronwall, “The Gamma Function in the Integral Calculus,” Ann. of Math., 20, 35–124 (1918). 10.2307/1967180

[3]

G. D. Birkhoff, “Note on the Gamma Function,” Bull. Amer. Math. Soc., 20, 1–10 (1913). 10.1090/s0002-9904-1913-02429-7

[4]

J. L. W. V. Jensen and T. H. Gronwall, “An Elementary Exposition of the Theory of the Gamma Function,” Ann. of Math., 17, 124–166 (1916). 10.2307/2007272

[5]

W. A. Khan, “A New Class of Degenerate Frobenius-Euler-Hermite Polynomials,” Adv. Stud. Contemp. Math. (Kyungshang), 28, 567–576 (2018).

[6]

T. Kim and D. S. Kim, “Degenerate Laplace Transform and Degenerate Gamma Function,” Russ. J. Math. Phys., 24, 241–248 (2017). 10.1134/s1061920817020091

[7]

T. Kim and G.-W. Jang, “A Note on Degenerate Gamma Function and Degenerate Stirling Number of the Second Kind,” Adv. Stud. Contemp. Math. (Kyungshang), 28, 207–214 (2018).

[8]

D. S. Kim, T. Kim, and G.-W. Jang, “A Note on Degenerate Stirling Numbers of the First Kind,” Proc. Jangjeon Math. Soc., 21, 393–404 (2018).

[9]

T. Kim, D. S. Kim, and H.-I. Kwon, “A Note on Degenerate Stirling Numbers and Their Applications,” Proc. Jangjeon Math. Soc., 21, 195–203 (2018).

[10]

T. Kim,, “$$\lambda$$-Analogue of Stirling Numbers of the First Kind,” Adv. Stud. Contemp. Math. (Kyungshang), 27, 423–429 (2017).

[11]

T. Kim, D. S. Kim, J. Kwon, and H. Lee, “A Note on Degenerate Gamma Random Variables,” Revista Edu., 388, 39–44 (2020).

[12]

Y. Kim, B. M. Kim, L.-C. Jang, and J. Kwon, “A Note on Modified Degenerate Gamma and Laplace Transformation,” Symmetry, 10, (2018).

[13]

D. V. Kruchinin and V. V. Kruchinin, “Explicit Formula for Reciprocal Generating Function and Its Application,” Adv. Stud. Contemp. Math. (Kyungshang), 29, 365–372 (2019).

[14]

E. L. Post, “The Generalized Gamma Functions,” Ann. of Math., 20, 202–217 (1919). 10.2307/1967871

[15]

G. Rahman, K.S. Nisar, T. Kim, S. Mubeen, and M. Arshad, “Inequalities Involving Extended $$k$$-Gamma and $$k$$-Beta Functions,” Proc. Jangjeon Math. Soc., 21, 143–153 (2018).

[16]

E. D. Rainville, Special Functions, The Macmillan Co., New York (1960).

[17]

E. D. Rainville, Special Functions, Bronx, New York (1971).

[18]

E. D. Rainville, “Recent Publications and Presentations: Solved Problems: Gamma and Beta Functions, Legendre Polynomials, Bessel Functions,” Amer. Math. Monthly, 71, (1964). 10.2307/2311961

[19]

G. Rasch, “Notes on the Gamma-Function,” Ann. of Math., 32, 591–599 (1931). 10.2307/1968254

[20]

L. M. Upadhyaya, “On the Degenerate Laplace Transforms IV,” Inter. J. Eng. Sci. Res., 6, 198–209 (2018). 10.22161/ijaers.5.12.28

[21]

P. Vassilev, “On an Estimate from above for the Remainder Sum of Certain Series Related to Euler’s Gamma Function,” Adv. Stud. Contemp. Math. (Kyungshang), 24, 109–128 (2014).

[22]

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, Cambridge University Press, Cambridge (1996).

Cited By

42

Mathematical modelling of photovoltaic systems derived from Taylor series expansion of degenerate exponential functions

Hasan Mithat Delibaş, Necip Fazil Yilmaz · 2026

Solar Energy

Novel series representation of degenerate gamma function with formulation of new generalized kinetic equation

Asifa Tassaddiq, Rabab Alharbi · 2025

Mathematical and Computer Modelling...

Some identities on truncated polynomials associated with Lah-Bell polynomials

Lingling Luo, Yuankui Ma · 2023

Applied Mathematics in Science and...

On degenerate gamma matrix functions and related functions

Mohamed Akel, Ahmed Bakhet · 2022

Linear and Multilinear Algebra

Degenerate Whitney Numbers of First and Second Kind of Dowling Lattices

T. Kim, D. S. Kim · 2022

Russian Journal of Mathematical Phy...

Metrics

42

Citations

22

References

Details

Published: Jul 01, 2020
Vol/Issue: 27(3)
Pages: 352-358
License: View

Authors

Cite This Article

T. Kim, D. S. Kim (2020). Note on the Degenerate Gamma Function. Russian Journal of Mathematical Physics, 27(3), 352-358. https://doi.org/10.1134/s1061920820030061

Note on the Degenerate Gamma Function

You May Also Like