On (p, q) and (q, k)-extensions of a double-inequality bounding a ratio of Gamma functions

Kwara Nantomah; Edward Prempeh; Stephen Boakye Twum

doi:10.36753/mathenot.421447

EN

On (p, q) and (q, k)-extensions of a double-inequality bounding a ratio of Gamma functions

Abstract

In this paper, the authors present the (p, q) and (q, k)-extensions of a double inequality involving a ratio of Gamma functions. The method is based on some monotonicity properties of certain functions associated with the (p, q) and (q, k)-extensions of the Gamma function.

Keywords

Gamma function, psi function, inequality, (pˏ q)-extension, (qˏk)-extension

References

[1] C. Alsina and M. S. Tomás, A geometrical proof of a new inequality for the gamma function, J. Ineq. Pure Appl. Math., 6(2)(2005), Art. 48.
[2] T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976.
[3] R. Díaz and E. Pariguan, On hypergeometric functions and Pachhammer k-symbol, Divulgaciones Matemtícas, 15(2)(2007), 179-192.
[4] R. Díaz and C. Teruel, q, k-generalized gamma and beta functions, J. Nonlin. Math. Phys., 12(2005), 118-134.
[5] F. H. Jackson, On a q-Definite Integrals, Quarterly Journal of Pure and Applied Mathematics, 41(1910), 193-203.
[6] V. Krasniqi and F. Merovci, Some Completely Monotonic Properties for the (p, q)-Gamma Function, Mathematica Balkanica, New Series, 26(2012), Fasc. 1-2.
[7] K. Nantomah, Some Inequalities for the Ratios of Generalized Digamma Functions, Advances in Inequalities and Applications, 2014(2014), Article ID 28.
[8] K. Nantomah and M. M. Iddrisu, The k-analogue of some inequalities for the Gamma function, Electron. J. Math. Anal. Appl., 2(2)(2014), 172-177.
[9] K. Nantomah, E. Prempeh and S. B. Twum, The (q, k)-extension of some Gamma function inequalities, Konuralp Journal of Mathematics, 4(1)(2016), 148-154.
[10] N. V. Vinh and N. P. N. Ngoc, An inequality for the Gamma Function, International Mathematical Forum, 4(28)(2009), 1379-1382.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Kwara Nantomah

Edward Prempeh This is me

Stephen Boakye Twum This is me

Publication Date

October 30, 2016

Submission Date

January 16, 2016

Acceptance Date

-

Published in Issue

Year 2016 Volume: 4 Number: 2

DOI

https://doi.org/10.36753/mathenot.421447

IZ

https://izlik.org/JA82BA66AC

APA

Nantomah, K., Prempeh, E., & Twum, S. B. (2016). On (p, q) and (q, k)-extensions of a double-inequality bounding a ratio of Gamma functions. Mathematical Sciences and Applications E-Notes, 4(2), 23-28. https://doi.org/10.36753/mathenot.421447

AMA

1.Nantomah K, Prempeh E, Twum SB. On (p, q) and (q, k)-extensions of a double-inequality bounding a ratio of Gamma functions. Math. Sci. Appl. E-Notes. 2016;4(2):23-28. doi:10.36753/mathenot.421447

Chicago

Nantomah, Kwara, Edward Prempeh, and Stephen Boakye Twum. 2016. “On (p, Q) and (q, K)-Extensions of a Double-Inequality Bounding a Ratio of Gamma Functions”. Mathematical Sciences and Applications E-Notes 4 (2): 23-28. https://doi.org/10.36753/mathenot.421447.

EndNote

Nantomah K, Prempeh E, Twum SB (October 1, 2016) On (p, q) and (q, k)-extensions of a double-inequality bounding a ratio of Gamma functions. Mathematical Sciences and Applications E-Notes 4 2 23–28.

IEEE

[1]K. Nantomah, E. Prempeh, and S. B. Twum, “On (p, q) and (q, k)-extensions of a double-inequality bounding a ratio of Gamma functions”, Math. Sci. Appl. E-Notes, vol. 4, no. 2, pp. 23–28, Oct. 2016, doi: 10.36753/mathenot.421447.

ISNAD

Nantomah, Kwara - Prempeh, Edward - Twum, Stephen Boakye. “On (p, Q) and (q, K)-Extensions of a Double-Inequality Bounding a Ratio of Gamma Functions”. Mathematical Sciences and Applications E-Notes 4/2 (October 1, 2016): 23-28. https://doi.org/10.36753/mathenot.421447.

JAMA

1.Nantomah K, Prempeh E, Twum SB. On (p, q) and (q, k)-extensions of a double-inequality bounding a ratio of Gamma functions. Math. Sci. Appl. E-Notes. 2016;4:23–28.

MLA

Nantomah, Kwara, et al. “On (p, Q) and (q, K)-Extensions of a Double-Inequality Bounding a Ratio of Gamma Functions”. Mathematical Sciences and Applications E-Notes, vol. 4, no. 2, Oct. 2016, pp. 23-28, doi:10.36753/mathenot.421447.

Vancouver

1.Kwara Nantomah, Edward Prempeh, Stephen Boakye Twum. On (p, q) and (q, k)-extensions of a double-inequality bounding a ratio of Gamma functions. Math. Sci. Appl. E-Notes. 2016 Oct. 1;4(2):23-8. doi:10.36753/mathenot.421447