The Journal of the Indian Mathematical Society

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Multi-Indexed Whittaker Function and its Properties


Affiliations
1 Department of Mathematics, Amity Institute of Applied Sciences, Amity University, Noida, India
2 Department of Mathematics, Siddharth University, Kapilvastu, India
     

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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.
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  • 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.


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  • Multi-Indexed Whittaker Function and its Properties

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Authors

Savita Panwar
Department of Mathematics, Amity Institute of Applied Sciences, Amity University, Noida, India
Prakriti Rai
Department of Mathematics, Siddharth University, Kapilvastu, India

Abstract


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.

References