Some bounds for the k-generalized digamma function

Hesham Moustafa; Mansour Mahmoud; Ahmed Talat

doi:10.31801/cfsuasmas.1230703

Araştırma Makalesi

Some bounds for the k-generalized digamma function

Yıl 2023, Cilt: 72 Sayı: 4, 1126 - 1140, 29.12.2023

Hesham Moustafa , Mansour Mahmoud Ahmed Talat

https://doi.org/10.31801/cfsuasmas.1230703

Öz

We presented some monotonicity properties for the k-generalized digamma function $\psi_{k}(h)$ and we established some new bounds for $\psi_{k}^{(s)}(h),$ $s\in \mathbb{N}\cup\{0\},$ which refine recent results

Anahtar Kelimeler

Gamma function, digamma function, polygamma function, completely monotonic function, asymptotic expansion, inequalities

Kaynakça

Abramowitz, M., Stegun, I. A., Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover, New York, 1965.
Batir, N., Sharp bounds for the psi function and harmonic numbers, Math. Inequal.Appl, 14(4) (2011), 917-925. http://files.ele-math.com/abstracts/mia-14-77-abs.pdf
Coffey, M. W., One integral in three ways: moments of a quantum distribution, J. Phys. A: Math. Gen., 39 (2006), 1425-1431. https://doi.org/10.1088/0305-4470/39/6/015
Diaz, R., Pariguan, E., On hypergeometric functions and k−Pochhammer symbol, Divulg. Mat., 15(2) (2007), 179-192. https://doi.org/10.48550/arXiv.math/0405596
Guo, B.-N., Qi, F., Sharp inequalities for the psi function and harmonic numbers, Analysis, 34(2) (2014), 201-208. DOI 10.1515/anly-2014-0001.
Kokologiannaki, C. G., Krasniqi, V., Some properties of the k-gamma function, Le Matematiche, 68(1) (2013), 13-22. DOI 10.4418/2013.68.1.2
Mansour, M., Determining the k-generalized gamma function Γk(x) by functional equations, Int. J. Contemp. Math. Sciences, 4(21) (2009), 653-660. http://www.m-hikari.com/ijcmspassword2009/21-24-2009/mansourIJCMS21-24-2009.pdf
Miller, A. R., Summations for certain series containing the digamma function, J. Phys. A: Math. Gen., 39 (2006), 3011-3020. DOI 10.1088/0305-4470/39/12/010
Moustafa, H., Almuashi, H., Mahmoud, M., On some complete monotonicity of functions related to generalized k−gamma function, J. Math., 2021 (2021), 1-9. https://doi.org/10.1155/2021/9941377
Muqattash, I., Yahdi, M., Infinite family of approximations of the digamma function, Math. Comput. Modelling, 43(11-12) (2006), 1329-1336. https://doi.org/10.1016/j.mcm.2005.02.010
Nantomah, K., Iddrisu, M. M., The k-analogue of some inequalities for the gamma function, Electron. J. Math. Anal. Appl., 2(2) (2014), 172-177.
Nantomah, K., Nisar, K. S., Gehlot, K. S., On a k-extension of the Nielsen’s (beta)-function, Int. J. Nonlinear Anal. Appl., 9(2) (2018), 191-201. http://dx.doi.org/10.22075/ijnaa.2018.12972.1668
Qi, F., Guo, S.-L., Guo, B.-N., Complete monotonicity of some functions involving polygamma functions, J. Comput. Appl. Math., 233 (2010), 2149-2160. https://doi.org/10.1016/j.cam.2009.09.044
Qiu, S.-L., Vuorinen, M., Some properties of the gamma and psi functions with applications, Math. Comp., 74(250) (2005), 723-742. DOI 10.1090/S0025-5718-04-01675-8
Widder, D. V., The Laplace Transform, Princeton University Press, Princeton, 1946.
Wilkins, B. D., Hromadka, T. V., Using the digamma function for basis functions in mesh-free computational methods, Engineering Analysis with Boundary Elements, 131 (2021), 218-227. https://doi.org/10.1016/j.enganabound.2021.06.004
Yildirim, E., Monotonicity properties on k−digamma function and its related inequalities, J. Math. Inequal., 14(1) (2020), 161-173. https://doi.org/10.7153/jmi-2020-14-12
Yildirim, E., Ege, I., On k-analogues of digamma and polygamma functions, J. Class. Anal., 13(2) (2018), 123-131. https://doi.org/10.7153/jca-2018-13-08
Yin, L., Huag, L. G., Song, Z. M., Dou, X. K., Some monotonicity properties and inequalities for the generalized digamma and polygamma functions, J. Inequal. Appl., 1 (2018), 249. https://doi.org/10.1186/s13660-018-1844-2
Yin, L., Zhang, J., Lin, X., Complete monotonicity related to the k-polygamma functions with applications, Ad. Diff. Eq., (2019), 1-10. https://doi.org/10.1186/s13662-019-2299-6

Yıl 2023, Cilt: 72 Sayı: 4, 1126 - 1140, 29.12.2023

Hesham Moustafa , Mansour Mahmoud Ahmed Talat

https://doi.org/10.31801/cfsuasmas.1230703

Öz

Kaynakça

Abramowitz, M., Stegun, I. A., Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover, New York, 1965.
Batir, N., Sharp bounds for the psi function and harmonic numbers, Math. Inequal.Appl, 14(4) (2011), 917-925. http://files.ele-math.com/abstracts/mia-14-77-abs.pdf
Coffey, M. W., One integral in three ways: moments of a quantum distribution, J. Phys. A: Math. Gen., 39 (2006), 1425-1431. https://doi.org/10.1088/0305-4470/39/6/015
Diaz, R., Pariguan, E., On hypergeometric functions and k−Pochhammer symbol, Divulg. Mat., 15(2) (2007), 179-192. https://doi.org/10.48550/arXiv.math/0405596
Guo, B.-N., Qi, F., Sharp inequalities for the psi function and harmonic numbers, Analysis, 34(2) (2014), 201-208. DOI 10.1515/anly-2014-0001.
Kokologiannaki, C. G., Krasniqi, V., Some properties of the k-gamma function, Le Matematiche, 68(1) (2013), 13-22. DOI 10.4418/2013.68.1.2
Mansour, M., Determining the k-generalized gamma function Γk(x) by functional equations, Int. J. Contemp. Math. Sciences, 4(21) (2009), 653-660. http://www.m-hikari.com/ijcmspassword2009/21-24-2009/mansourIJCMS21-24-2009.pdf
Miller, A. R., Summations for certain series containing the digamma function, J. Phys. A: Math. Gen., 39 (2006), 3011-3020. DOI 10.1088/0305-4470/39/12/010
Moustafa, H., Almuashi, H., Mahmoud, M., On some complete monotonicity of functions related to generalized k−gamma function, J. Math., 2021 (2021), 1-9. https://doi.org/10.1155/2021/9941377
Muqattash, I., Yahdi, M., Infinite family of approximations of the digamma function, Math. Comput. Modelling, 43(11-12) (2006), 1329-1336. https://doi.org/10.1016/j.mcm.2005.02.010
Nantomah, K., Iddrisu, M. M., The k-analogue of some inequalities for the gamma function, Electron. J. Math. Anal. Appl., 2(2) (2014), 172-177.
Nantomah, K., Nisar, K. S., Gehlot, K. S., On a k-extension of the Nielsen’s (beta)-function, Int. J. Nonlinear Anal. Appl., 9(2) (2018), 191-201. http://dx.doi.org/10.22075/ijnaa.2018.12972.1668
Qi, F., Guo, S.-L., Guo, B.-N., Complete monotonicity of some functions involving polygamma functions, J. Comput. Appl. Math., 233 (2010), 2149-2160. https://doi.org/10.1016/j.cam.2009.09.044
Qiu, S.-L., Vuorinen, M., Some properties of the gamma and psi functions with applications, Math. Comp., 74(250) (2005), 723-742. DOI 10.1090/S0025-5718-04-01675-8
Widder, D. V., The Laplace Transform, Princeton University Press, Princeton, 1946.
Wilkins, B. D., Hromadka, T. V., Using the digamma function for basis functions in mesh-free computational methods, Engineering Analysis with Boundary Elements, 131 (2021), 218-227. https://doi.org/10.1016/j.enganabound.2021.06.004
Yildirim, E., Monotonicity properties on k−digamma function and its related inequalities, J. Math. Inequal., 14(1) (2020), 161-173. https://doi.org/10.7153/jmi-2020-14-12
Yildirim, E., Ege, I., On k-analogues of digamma and polygamma functions, J. Class. Anal., 13(2) (2018), 123-131. https://doi.org/10.7153/jca-2018-13-08
Yin, L., Huag, L. G., Song, Z. M., Dou, X. K., Some monotonicity properties and inequalities for the generalized digamma and polygamma functions, J. Inequal. Appl., 1 (2018), 249. https://doi.org/10.1186/s13660-018-1844-2
Yin, L., Zhang, J., Lin, X., Complete monotonicity related to the k-polygamma functions with applications, Ad. Diff. Eq., (2019), 1-10. https://doi.org/10.1186/s13662-019-2299-6

Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Matematik
Bölüm	Research Article
Yazarlar	Hesham Moustafa 0000-0002-2792-6239 Mansour Mahmoud 0000-0002-5918-1913 Ahmed Talat 0000-0001-7702-8093
Yayımlanma Tarihi	29 Aralık 2023
Gönderilme Tarihi	6 Ocak 2023
Kabul Tarihi	16 Eylül 2023
Yayımlandığı Sayı	Yıl 2023 Cilt: 72 Sayı: 4

Kaynak Göster

APA	Moustafa, H., Mahmoud, M., & Talat, A. (2023). Some bounds for the k-generalized digamma function. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 72(4), 1126-1140. https://doi.org/10.31801/cfsuasmas.1230703
AMA	Moustafa H, Mahmoud M, Talat A. Some bounds for the k-generalized digamma function. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Aralık 2023;72(4):1126-1140. doi:10.31801/cfsuasmas.1230703
Chicago	Moustafa, Hesham, Mansour Mahmoud, ve Ahmed Talat. “Some Bounds for the K-Generalized Digamma Function”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, sy. 4 (Aralık 2023): 1126-40. https://doi.org/10.31801/cfsuasmas.1230703.
EndNote	Moustafa H, Mahmoud M, Talat A (01 Aralık 2023) Some bounds for the k-generalized digamma function. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72 4 1126–1140.
IEEE	H. Moustafa, M. Mahmoud, ve A. Talat, “Some bounds for the k-generalized digamma function”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 72, sy. 4, ss. 1126–1140, 2023, doi: 10.31801/cfsuasmas.1230703.
ISNAD	Moustafa, Hesham vd. “Some Bounds for the K-Generalized Digamma Function”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72/4 (Aralık 2023), 1126-1140. https://doi.org/10.31801/cfsuasmas.1230703.
JAMA	Moustafa H, Mahmoud M, Talat A. Some bounds for the k-generalized digamma function. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:1126–1140.
MLA	Moustafa, Hesham vd. “Some Bounds for the K-Generalized Digamma Function”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 72, sy. 4, 2023, ss. 1126-40, doi:10.31801/cfsuasmas.1230703.
Vancouver	Moustafa H, Mahmoud M, Talat A. Some bounds for the k-generalized digamma function. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(4):1126-40.