Refine your search

Collections

Co-Authors

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z **All**

### Chaturvedi, Aparna

- Some Properties of Extended Hypergeometric Function and its Transformations

Abstract Views :81 |
PDF Views:2

1 Department of Mathematics, Amity Institute of Applied Sciences Amity University, Noida, IN

#### Authors

**Affiliations**

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: 305-312#### Abstract

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 :20 |
PDF Views:1

1 Department of Mathematics, Amity Institute of Applied Sciences, Amity University, Noida, IN

#### Authors

**Affiliations**

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: 9-21#### Abstract

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 functions#### Keywords

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

- T. M. Apostol, On the Lerch Zeta function, Pacific J. Math., 1(1951), 161-167.
- E. T. Bell, Exponential polynomials, Ann. Math., 35(1934), 258-277.
- G. Dattoli, B. Germano and P. E. Ricci, Hermite polynomials with more than two variables and associated bi-orthogonal functions, Integral Transforms and Special Functions, 20(1) (2009), 17-22.
- 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.
- M. A. Pathan and W. A. Khan, Some new classes of generalized Hermite-based Apostol-Euler and Apostol-Genocchi polynomials, Fasciculi Mathematici, 55(2015), 153-170, DOI: 10.1515/fascmath2015-0020.
- E. D. Rainville, Special Functions, The Macmillan Company, New York, 1960.
- H. M. Srivastava and H. L. Manocha, Atreatise on Generating Functions, Halsted, New York, 1984.
- H. M. Srivastava, Some formulas for the Bernoulli and Euler polynomials at rational arguments, Math. Proc. Cambridge Philos. Soc. 129 (2000), 77-84.
- R. Tremblay, S. Gaboury and B. J. Fugere, Some new classes of generalized Apostol-Euler and Apostol-Genocchi polynomials, Int. J. Math and Math. Sci. (2012), DOI:10.1155/2012/182785.
- 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.