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Rai, Prakriti
- Some Properties of Extended Hypergeometric Function and its Transformations
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Authors
Affiliations
1 Department of Mathematics, Amity Institute of Applied Sciences Amity University, Noida, IN
1 Department of Mathematics, Amity Institute of Applied Sciences Amity University, Noida, IN
Source
The Journal of the Indian Mathematical Society, Vol 85, No 3-4 (2018), Pagination: 305-312Abstract
There emerges different extended versions of Beta function and hypergeometric functions containing extra parameters. We obtain some properties of certain functions like extended Generalized Gauss hypergeometric functions, extended Confluent hypergeometric functions including transformation formulas, Mellin transformation for the generalized extended Gauss hypergeometric function in one, two and more variables.Keywords
Extended Gamma and Extended Beta Functions, Extended Gauss Hypergeometric Functions, Extended Confluent Hypergeometric Functions, Mellin Transforms.
References
- L.C. Andrews, Special Functions for Engineers and Applied Mathematicians, New York, McMillan (1985).
- M.A. Chaudhry and S.M. Zubair, Generalized incomplete gamma functions with applications, J. Comput. Appl. Math. 55 (1994), 99-124.
- M.A. Chaudhry, A. Qadir M. Raque and S.M. Zubair, Extension of Euler's beta function, J. Comput. Appl. Math. 78 (1997), 19-32.
- L. Minjie, A Class of Extended Hypergeometric Functions and Its Applications, arXiv:1302.2307v1, [math.CA]. 2013.
- E. Ozergin, M.A. Ozarslan and A. Altin, Extension of gamma, beta and hypergeometric functions, J. Comput. Appl. Math., 235 (2011), 4601-4610.
- M.A. Ozarslan and E. Ozergin, Some generating relations for extended hypergeometric function via generalized fractional derivative operator, Math. Comput. Model., 52 (2010), 1825-1833.
- H.M. Srivastava, R.K. Parmar and P. Chopra, A Class of Extended Fractional Derivative Operators and Associated Generating Relations Involving Hypergeometric Functions, Axioms 2012, I, 238-258.
- Generalized Hermite-Based Apostol-Bernoulli, Euler, Genocchi Polynomials and their Relations
Abstract Views :471 |
PDF Views:1
Authors
Affiliations
1 Department of Mathematics, Amity Institute of Applied Sciences, Amity University, Noida, IN
1 Department of Mathematics, Amity Institute of Applied Sciences, Amity University, Noida, IN
Source
The Journal of the Indian Mathematical Society, Vol 87, No 1-2 (2020), Pagination: 9-21Abstract
In this paper, we have generalized Apostol-Hermite-Bernoullli polynomials, Apostol-Hermite-Euler polynomials and Apostol-Hermite-Genocchi polynomials. We have shown that there is an intimate connection between these polynomials and derived some implicit summation formulae by applying the generating functionsKeywords
2010 Mathematics Subject Classification. Primary 54C40, 14E20; Secondary 46E25, 20C20.
Apostol-Hermite-Bernoullli Polynomials, Apostol-Hermite-Euler Polynomials and Apostol-Hermite-Genocchi Polynomials, Summation Formulae, Symmetric Identities.
References
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- Q. M. Luo, Fourier expansions and integral representations for the Apostol-Bernoulli and ApostolEuler polynomials, Math. of Comp. 78 (2009), 2193-2208.
- Q. M. Luo, Fourier expansions and integral representations for the Genocchi polynomials, J. Integer Seq. 12 (2009), 1-9.
- Q. M. Luo, q-extension for the Apostol-Genocchi polynomials, Gen. Math. 17 (2009), 113-125.
- Q. M. Luo, Some formulas for the Apostol-Euler polynomials associated with Hurwitz zeta function at rational arguments, Applicable Analysis and Discrete Mathematics 3(2) (2009), 336-346.
- Q. M. Luo, The multiplication formulas for the Apostol-Bernoulli and Apostol-Euler polynomials of higher order, Integral Transform and Special Functions, 20(5-6) (2009), 377-391.
- Q. M. Luo, Extension for the Genocchi polynomials and its Fourier expansions and integral representations, Osaka J. Math. 48 (2011), 291-310.
- Q. M. Luo and H. M. Srivastava, Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials, J. Math. Anal. Appl., 308(2005), 290-302.
- Q. M. Luo and H. M. Srivastava, Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials, Computers and Mathematics with Applications, 51(3-4) (2006), 631-642.
- Q. M. Luo and H. M. Srivastava, Some generalizations of the Apostol-Genocchi polynomials and the Stirling numbers of the second kind, Applied Math. & Comput. 217(12) (2011), 5702-5728.
- M. A. O¨ zarslan, Hermite-based unified Apostol-Bernoulli, Euler and Genocchi polynomials, Adv. Diff. Eq. (2013), 116, DOI: 10.1186/1687-1847-2013-116.
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- R. Tremblay, S. Gaboury and B. J. Fugere, A further generalization of Apostol-Bernoulli polynomials and related polynomials, Honam Math. J. 34 (2012), 311-326.
- A Generalization of Class of Humbert - Hermite Polynomials
Abstract Views :336 |
PDF Views:0
Authors
Saniya Batra
1,
Prakriti Rai
2
Affiliations
1 Department of Mathematics, Institute of Applied Sciences, Amity University, Noida, IN
2 Department of Mathematics, Siddharth University, Kapilvastu, India Siddharth Nagar, IN
1 Department of Mathematics, Institute of Applied Sciences, Amity University, Noida, IN
2 Department of Mathematics, Siddharth University, Kapilvastu, India Siddharth Nagar, IN
Source
The Journal of the Indian Mathematical Society, Vol 89, No 3-4 (2022), Pagination: 227-236Abstract
A generalization of Humbert-Hermite polynomials is defined in this paper. Moreover, several generalizations of Hermite-Gegenbauer polynomials, Hermite-Legendre and Hermite-Chebyshev polynomials are established.
Keywords
Hermite Polynomials, Humbert Polynomials, Gegenbauer Polynomials, Legendre Polynomials, Chebyshev Polynomials, Hypergeometric Function.References
- E. T. Bell, Exponential polynomials, Ann. of Math., 35(1934), 258-277.
- A. Chaturvedi, and Rai, P., Generalized Hermite-based Apostol-Bernoulli, Euler, Genocchi polynomials and their relations, Journal of Indian Mathematical Society, 87(1-2)(2020), 9-21.
- J. Choi, Notes on formal manipulations ofdouble series, Commun. Korean Math. Soc., 18(4) (2003), 781-789.
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- M. A. Pathan and M. A. Khan, On polynomials associated with Humberts polynomials, Publ. Inst. Math., (Beograd), 62(76) (1997), 53–62.
- M. A. Pathan and N. U. Khan, A uni?ed presentation of a class of generalized Humbert Polynomials in two variables, ROMAI J., 11(2) (2015), 185–199.
- M. A. Pathan and W. Khan, On a class of Humbert-Hermite polynomials, Novi Sad J. Math., 51(1) (2021), 1–11.
- Y. Simsek and M. Acikgoz, A new generating function of (q?)Bernstein-type polynomials and their interpolation function, Abstract and Applied Analysis, 2010 (2010), Article ID 769095, 12 Pages.
- Multi-Indexed Whittaker Function and its Properties
Abstract Views :285 |
PDF Views:0
Authors
Affiliations
1 Department of Mathematics, Amity Institute of Applied Sciences, Amity University, Noida, IN
2 Department of Mathematics, Siddharth University, Kapilvastu, IN
1 Department of Mathematics, Amity Institute of Applied Sciences, Amity University, Noida, IN
2 Department of Mathematics, Siddharth University, Kapilvastu, IN
Source
The Journal of the Indian Mathematical Society, Vol 90, No 1-2 (2023), Pagination: 115-124Abstract
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
- 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.
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