Area of Specialization: Special Functions:
Worked to obtain new Erdèlyi type integrals and their q-analogues; extensions of Bailey’s transform and new Bailey type transforms and their applications to investigate new hypergeometric, q-hypergeometric and Rogers-Ramanujan type identities; new q-series expansions applicable to Bi-orthogonal rational functions.
Research Interest:
Applications of Special Functions: Generalized, Elliptic and q-Hypergeomeric functions; Orthogonal polynomials and Bi-orthogonal rational functions; Rogers-Ramanujan type and other combinatorial identities from q-series; Graph theory, Discrete Mathematics.
Publication:
International: 05
-
In Journal of Computational and Applied Mathematics, Elsevier,
Netherlands
in 2003
-
In
International Journal of Mathematics and Mathematical Sciences,
Hindawi Pub., Texas, USA
in 2005
- In
Journal of
Mathematical Analysis and Applications, Elsevier, San Diego, CA,
USA in 2006
- In
Applied
Mathematics and Computation, Elsevier, New York in 2007
- In
Mathematics ArXive via
http://aps.arxiv.org/abs/math.CA/0701192 in
2007
National: 01
Workshop/ Seminar:
- As an Invited Speaker, I delivered a Series of Lectures on “Elliptic Hypergeometric Series” in a Workshop on ‘Ramanujan’s Mathematics’ organized by National Academy of Sciences, India, Allahabad (NASI) on Wednesday, 22-12-2010, on the occasion of Mathematics Day, 22nd December (Ramanujan’s Birthday).
- Presented a paper entitled “Application of Extended Bailey’s Transform to Elliptic Hypergeometric Series” in a Conference on Special Functions and their Applications & Symposium on Computational and Biological Mathematics held at Jiwaji University [Sponsored by UGC, DST, CSIR, MPCST] ( June 21 – 23, 2010, Gwalior), and according to Google search and discussion among members of the society this paper was considered as the first contribution from india for “elliptic hypergeometric series”.
- Presented a paper entitled “Extensions of Certain Classical Integrals of Erdélyi for Gauss Hypergeometric Functions” in the International Conference on Special Functions and Their Applications, held at the Institute of Mathematical Sciences [Sponsored by SSFA, India & OPSF activity group of SIAM] ( September 23 – 27, 2002, Chennai).
- Presented a paper entitled “On Double Series Analogues of Certain Well-poised Sums” in Indian Science Congress Association’s 89th Session, held at University of Lucknow ( January 03 – 07, 2002, Lucknow).
- Attended the XIII annual conference of “ Rajasthan Ganita Parishad and Symposium ”on Dec. 14-15, 2001 at Department of Mathematics & Statistics, University College of Science, MLSU, Udaipur
Research
Achievements/Awards:
- Junior Research Fellowship and Senior Research Fellowship
awarded by Council of Scientific and Industrial Research (CSIR),
New Delhi after being selected from the National level
CSIR-UGC-NET-JRF Exam
- Awarded REVIEWERSHIP for MATHEMATICAL REVIEWS by AMERICAN
MATHEMATICAL SOCIETY in 2006 and has reviewed 15 articles so far
- BIOGRAPHY published in Marquis Who’s Who in the World-2007, 24th
edition among 50, 000 most accomplished persons from all over
the world
- Member of American Mathematical Society, USA
- Life Member: Society for Special Functions and Their Applications (SSFA), Lucknow, India
Recently reviewed Five research articles for Mathematical Reviews(AMS), USA:
Author(s) |
University/Nation |
Title |
Pages |
Journal detail |
Krasniqi, Valmir; Shabani, Armend Sh. |
University of Prishtina,
Republic of Kosova |
On some Feng Qi type h-integral inequalities. |
06 |
Int. J. Open Problems Compt. Math. |
Avkhadiev F. G., Wirths K.J.
|
Kazan State University, Russia
|
Weighted Hardy Inequalities with Sharp Constants
|
07 |
Lobachevskii Journal of Mathematics |
Dominique Foata, Guo-Niu Han |
Institut Lothaire,
Univetsite Louis Pasteur, France |
The doubloon polynomial triangle |
20 |
Ramanujan J, Springer. |
Lidia Fernandez, Teresa E. Perez, Miguel A, Pinar |
Universidad de Granada, Spain |
Orthogonal polynomials in two variables as solutions of higher order partial differential equations |
14 |
Journal of Approximation Theory, Elsevier. |
Masahiko Ito |
Tokyo denki University, Japan |
Three-term relations between interpolation polynomials for BCn –type basic hypergeometric series |
35 |
Advances in Mathematics |
|
