Certain properties of the Wright function
Bhaven V. Zalazalabhaven1550@gmail.comDepartment of MathematicsSardar Patel UniversityVallabh Vidyanagar, Gujarat, 388120, IndiaView full profile → , *Jyotindra C. PrajapatiCorresponding authordrjyotindra18@gmail.comDepartment of MathematicsSardar Patel UniversityVallabh Vidyanagar, Gujarat, 388120, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Feb 2025
- Published Online:
- 07 Apr 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2380
- Pages:
- 909–925
Abstract
Keywords
Subject Classifications
References
[1] E. M. Wright, “On the Coefficients of Power Series Having Exponential Singularities”, J. London Math. Soc., s1-8, pp.71-79 (1933).
[2] E. M. Wright, “The Asymptotic Expansion of the Generalized Bessel Function”, Proc. Lond. Math. Soc., s2-38: pp.257-270 (1935), https://doi.org/10.1112/plms/s2-38.1.257.
[3] E. M. Wright, “The generalized Bessel function of order greater than one”, Q. J. Math., vol. 11, Issue 1, pp.36-48 (1940), https://doi.org/10.1093/qmath/os-11.1.36.
[4] E. M. Wright, “The Asymptotic Expansion of the Generalized Hypergeometric Function”, J. London Math. Soc. (2), s1-10, pp.286-293 (1935).
[5] K. S. Gehlot, J. C. Prajapati, and B. P. Patel, “Differential recurrence relation of Generalized K- Wright function”, Int. J. Pure Appl. Math., vol. 87, no. 4, pp. 611-619 (2013), http://dx.doi.org/10.12732/ijpam.v87i4.10.
[6] Y. Luchko, “The Wright function and its applications”, vol. 1, Basic Theory edited by Anatoly Kochubei and Yuri Luchko, pp. 241-268.Berlin, Boston: De Gruyter (2019), https://doi.org/10.1515/9783110571622-010.
[7] K. Mehrez, “New Integral representations for the Fox-Wright functions and its applications”, J. Math. Anal. Appl., vol. 468, no. 2, pp.650-673 (2018), https://doi.org/10.1016/j.jmaa.2018.08.053.
[8] K. Mehrez, and S. M. Sitnik, “Functional inequalities for Fox-Wright functions”, Ramanujan J, vol. 50, pp. 263-287 (2019), https://doi.org/10.1007/s11139-018-0071-2.
[9] F. Mainardi, and A. Consiglio, “The Wright Functions of the Second Kind in Mathematical Physics”, Mathematics, vol. 8, no. 6, 2020, https://doi.org/10.3390/math8060884.
[10] R. Gorenflo, Y. Luchko, and F. Mainardi, “Wright functions as scale-invariant solutions of the diffusion-wave equation”, J. Comput. Appl. Math., vol. 118, no. 1, pp.175-191 (2000), https://doi.org/10.1016/S0377-0427(00)00288-0.
[11] Y. Singh, and R. S. Dubey, “Fractional calculus operator with generalize k-Mittag-Leffler function”, J. Interdiscip. Math., vol. 23, no. 2, pp. 545-553 (2020), https://doi.org/10.1080/09720502.2020.1731971.
[12] R. S. Dubey, Y. Singh, P. Agarwal, G. L. Saini, and V. Singh, “Some results on the new fractional derivative of generalized k-Wright function” J. Interdiscip. Math., vol. 23, no. 2, pp. 607-615 (2020), https://doi.org/10.1080/09720502.2020.1731981.
[13] Liya D’Costa, and N. Menaria, “Fractional calculus of extended k-generalized Mittag-Leffler function and its properties”, J. Interdiscip. Math., vol. 27, no. 8, pp. 1741-1748 (2024), https://doi.org/10.47974/JIM-2036.
[14] E. D. Rainville , Special functions, The Macmillan Company, (1960).
[15] A. Wiman, “Über den Fundamentalsatz in der Teorie der Funktionen Eα (x)”, Acta Math., vol. 29, pp.191-201 (1905), https://doi.org/10.1007/BF02403202.
[16] R. Gorenflo, A. Kilbas, F. Mainardi, and S. Rogosin, “The Two-Parametric Mittag-Leffler Function”, Mittag-Leffler Functions, Related Topics and Applications; Springer: Berlin, Germany, 2nd Edition, pp.63-113 (2020), https://doi.org/10.1007/978-3-662-61550-8_4.
[17] G. N. Watson, “A Treatise on the Theory of Bessel Functions”, Amer. Math. Monthly, vol. 30, no. 6, pp. 326-327 (1923), https://doi.org/10.2307/2300274.
[18] P. Van Mieghem, “The Mittag-Leffler function”, arXiv e-prints, pp. 105-107 (2020), arXiv:2005.13330[math.FA], https://ui.adsabs.harvard.edu/abs/2020arXiv200513330V.
[19] A. Apelblat and J. L. González-Santand, “The integral Mittag-Leffler, Whittaker and Wright functions”, Mathematics, vol. 9, no. 24 (2021), https://doi.org/10.3390/math9243255.
[20] L. Andrews, “Other Functions Defined by Integrals”, Special Functions of Mathematics for Engineers, Second Edition, pp. 109-140 (1997), https://doi.org/10.1117/3.270709.ch3.
[21] J. Riordan, “Combinatorial Identities”, Wiley Series in Probability and Mathematical Statistics, Wiley, (1968).




