Open Access
Subscription Access
Open Access
Subscription Access
Multi-Indexed Whittaker Function and its Properties
Subscribe/Renew Journal
In this paper, we have introduced the multi-indexed Whittaker function (3m-parameter) by using the extended confluent hypergeometric function which is defined in terms of multi-indexed (3m-parameter) Mittag-Leffler function. We derive some properties of multi-indexed (3m-parameter) Whittaker function such as its integral representations, derivative formula and Hankel transform.
Keywords
Extended Beta Function, Gauss Hypergeometric Function, Confluent Hypergeometric Function, Multi-Index Mittag-Leffler Function, Whittaker Function and Extended Whittaker Function.
Subscription
Login to verify subscription
User
Font Size
Information
- M. Ali, M. Ghayasuddin, W. A. Khan and K. S. Nisar, A novel Kind of the multi-index Beta, Gauss and confluent hypergeometric functions, J. Math. Computer Sci., 23 (2021), 145–154.
- M. A. Chaudhry, A. Qadir, H. M. Srivastava and R. B. Paris, Extended hypergeometric and confluent hypergeometric functions, Appl. Math. Comput., 159 (2004), 589–602.
- M. A. Chaudhry, A. Qadir, M. Rafique and S. M. Zubair, Extension of Euler’s beta function, J. Comput. Appl. Math., 78 (1997), 19–32.
- A. Erdelyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Table of Integral Transforms, Vol. 1, McGraw-Hill, New York, 1954.
- M. Ghayasuddin, N. U. Khan and M. Ali, A study of extended beta, Gauss and confluent hypergeometric functions, Inter. J. Appl. Math., 33 (2020), 01-13.
- V. S. Kiryakova, The multi-index Mittag-Leffler functions as an important class of special functions of fractional calculus, Comput. Math. Appl., 59 (2010), 1885–1895.
- V. S. Kiryakova, Multiple (multiindex) Mittag-Leffler functions and relations to generalized fractional calculus, J. Comput. Appl. Math., 118 (2000), 241–259.
- G. M. Mittag-Leffler, Sur la representation analytique d´une branche uniforme d´une fonction monogene, Acta Math., 29 (1905), 101–182.
- D. K. Nagar, R. A. M. V´asquez and A. K. Gupta, Properties of the extended Whittaker function, Progr. Appl. Math., 6(2) (2013), 70–80.
- J. Paneva-Konovska, Multi-index(3m-parametric) Mittag-Leffler functions and fractional calculus, C. R. Acad. Bulgare Sci., 64 (2011), 1089–1098.
- J. Paneva-Konovska, From Bessel to multi-index Mittag-Leffler functions: Enumerable families,series in them and convergence,World Scientific Publishing, London, 2016.
- J. Paneva-Konovska, A survey on Bessel type functions as multi-index Mittag-Leffler functions: Differential and integral relations, Int. J. Appl. Math., 32 (2019), 357–380.
- E. D. Rainville, Special functions, The Macmillan Company, New York,1960, Reprinted by Chelsea Publishing Company, Bronx, New York, 1971.
- M. Shadab, S. Jabee, J. Choi, An extended beta function and its application, Far East J. Math. Sci., 103 (2018), 235–251.
- H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press (Eills Horwood Limited; Chichester ), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1984.
- E. T. Whittaker, An expression of certain known functions as generalized hypergeometric functions, Bull. Amer. Math. Soc., 10(3) (1903), 125–134.
Abstract Views: 215
PDF Views: 0