A New Class of Integral Relations Involving General Class of Polynomials and I-Functions

Authors

  • Shilpi JAIN Department of Mathematics, Poornima College of Engineering, Jaipur 302002
  • Praveen AGARWAL Department of Mathematics, Anand Intenational College of Engineering, Jaipur 303012

Keywords:

I-function, general class of polynomials, Psi (or digamma) functions

Abstract

The aim of the present paper is to evaluate new integral relations involving a general class of polynomials and I-functions. The values of the relations are obtained in terms of the Psi functions y (z) (the logarithmic derivative of Γ(z)). These integral relations are unified in nature and act as a key formula from which we can obtain their special cases. For the sake of illustration, we record here some special cases of our main formulas which are also new and known. The formulas established here are basic in nature and are likely to find useful applications in the field of science and engineering.

doi:10.14456/WJST.2015.38

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Author Biography

Praveen AGARWAL, Department of Mathematics, Anand Intenational College of Engineering, Jaipur 303012

Academic Qualifications:
Ph.D. (2006): University of Rajasthan, Jaipur.
M. Phil (2003): University of Rajasthan, Jaipur.
M.Sc. (2000): University of Rajasthan, Jaipur.

Topic of Ph.D.:
Investigations in Generalized Laplace Transform Special Functions and Fractional Calculus.

Topic of M. Phil:
A Study of Convolution Integral Equations.   

Visits to foreign countries:
a)    Invited by TOBB University of Economics and Technology in Ankara, to give a talk at the International Conference on Applied Mathematics & Approximation Theory, (AMAT 2012) held from 17-20 May 2012 in the TOBB University of Economics and Technology in Ankara, (Turkey).

b)    Invited by Quaid-i-Azam University, Islamabad, to give a talk at the 13th INTERNATIONAL PURE MATHEMATICS CONFERENCE 2012, from 01-03 September 2012. ). (Wish to attend the conference in Islamabad).

c)    Invited by University of Gabes, Tunisie to give a talk at the International conference on “Orthogonal Polynomials Special functions and Applications” 2013, from 25-29 March 2013). (Wish to attend the conference in Islamabad).

Experience of guiding research:
Guiding and supervising the research work of Ph.D. students of the University of Sighania, Dr. K. N. Modi University, Suresh Gyan Vihar University, Rajasthan, since 2009. Two candidates are working for Ph.D. degree under my supervision.   

Research Projects:
An research project entitled “A Study of fractional calculus (Derivatives and Integrals to an arbitrary order) and Mellin-Barnes Integral with applications” submitted to All India Council of Technical Education, New Delhi.( under processing)

Fields of research work:
(a) Integral transforms
(b) Special functions
(c) Integral equations
(d) Statistical distributions
(e) Fractional calculus
(f) Generalized functions
(g) Fractional deferential equations

Membership of learned societies
a)    Member of Who's Who in the World 2013 (30th pearl Anniversary Edition).
b)    Member of the American Biographical Institute’s prestigious honor “MAN OF THE YEAR 20120”. Of ABI.
c)    Member of “The Cambridge Certificate for Outstanding Educational Achievement” 2012, of IBC.
d)    Member of “2000 Outstanding Intellectuals of the 21st Century 2012” International biographical centre, Cambridge, England.
e)    Member of Governing Body of Anand International College of Engineering 2011.
f)    Member of Who's Who in Science and Engineering 2011-2012 (11th Edition).
g)    Member of Who's Who in the World 2012 (29th Edition).
h)    Life member of the International Association of Engineers (IAENG).
i)    Life member of “Rajasthan Academy of Physical Sciences”.
j)    Life member of “Society for Special Function and their Applications”.
k)    Editorial board member of the American Journal of Mathematics and Statistics.
l)    Editorial board member of the Asian Journal of Current Engineering & Math’s [AJCEM].
m)    Member of Scientific Committee & Editorial Review Board of World Academy of Science, Engineering and Technology, Science January 2012.
n)    Member of Editor Review Committee of International Journal of Scientific and Engineering Research (IJSER), Science January 2012.
o)    Member of Chief Technical Advisory Board of International Journal of Soft Computing and Engineering (IJSCE), Science January 2012.
p)    Member of Technical Editorial team of  Asian Journal of Mathematics & Statistics, Trends in Applied Sciences Research, Asian Journal of Scientific Research, Journal of Applied Sciences& Asian Journal of Applied Sciences, Science January 2012.
q)    Editorial board member of Shiv Shakti International Journal in Multidisciplinary and Academic Research (SSIJMAR) (ISSN 2278 – 5973), Science July 2012.
r)    Editorial board member of World Science Publisher, Science August 2012.

Experience as a Reviewer and Referee
a)    Evaluate the thesis of Doctor of Philosophy in Applied Mathematics for National College of Business Administration & Economics Lahore, Pakistan, on entitle “ Boundedness of Integral Operators Involving Generalized Hypergeometric Functions

b)    Since 2008, Reviewer for various International Journals like Asian-European Journal of Mathematics, European Journal of Pure and Applied Mathematics, Journal of Mathematical Research, Tamkong Journal of Mathematics, Korian Journal of Mathematics etc.

c)    Member of Scientific Committee & Editorial Review Board of World Academy of Science, Engineering and Technology, Science January 2012.

d)    Editor Review Committee member of International Journal of Scientific and Engineering Research, Science January 2012.

e)    CHIEF ADVISORY BOARD member of International Journal of Soft Computing and Engineering (IJSCE), Science January 2012.

f)    Member of Technical Editorial team of  Asian Journal of Mathematics & Statistics, Trends in Applied Sciences Research, Asian Journal of Scientific Research, Journal of Applied Sciences& Asian Journal of Applied Sciences, Science January 2012.

g)    Editorial board member of the American Journal of Mathematics and Statistics.

h)    Editorial board member of the Asian Journal of Current Engineering & Math’s [AJCEM].

Fellowships /Distinction/Prizes:
(a)    Awarded the American Biographical Institute’s prestigious honor “MAN OF THE YEAR 2012”by ABI, USA.

(b)    Awarded “The Cambridge Certificate for Outstanding Educational Achievement” 2012, by IBC, Great Britain.

(c)    Awarded the International Travel Grant from Human Resource Development Group Council of Scientific & Industrial Research (CSIR), to attend International Congress on Honor of Prof. H.M.Srivastava 2012 held from 23-26 July 2012 in the Uldag University, Bursa, (Turkey).  

(d)    Awarded the International Travel Grant from Ministry of Science and Technology, Department of Science and Technology Government of India (ITS) to attend International Conference on Applied Mathematics & Approximation Theory, AMAT 2012 held from 17-20 May 2012 in the TOBB University of Economics and Technology in Ankara, (Turkey).  

(e)    Awarded Research Fellowship from Malviya National Institute of Technology of Jaipur for three years during the session 2002-2004.

(f)    Caption of the Winner Cricket Team in M.Sc.2000.

(g)    Distinction in Mathematics B.Sc. Examination 1996.

(h)    Distinction in Mathematics Secondary Examination 1993.

(i)    Participation in Cultural activities at school level. Won several prizes

References

P Agarwal. A Study of New Trends and Analysis of Special Function. LAP Lambert Academic Publishing, 2013, p. 1-164.

P Agarwal. Certain multiple integral relations involving generalized Mellin-Barnes type of contour integral. Acta Univ. Apulensis Math. Inform. 2013; 33, 257-68.

P Agarwal. On a unified integral involving the product of Srivastava’s polynomials and generalized Mellin-Barnes type contour integral. Adv. Mech. Eng. Appl. 2012; 2, 158-61.

P Agarwal and CL Koul. Integrals involving product of H [x,y] and the generalized polynomials . Proc. Nat. Acad. Sci. India 2004; 74, 507-14.

P Agarwal. On multiple integral relations involving generalized Mellin-Barnes type of contour integral. Tamsui Oxf. J. Math. Sci. 2011; 27, 449-62.

J Choi and P Agarwal. Certain classes of infinite series deducible from Mellin-Barnes type of contour integrals. J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math. 2013; 20, 233-42.

P Agarwal. On a new theorem involving generalized Mellin-Barnes type of contour integral and Srivastava polynomials. J. Appl. Math. Stat. Inform. 2012; 8, 29-35.

P Agarwal, Certain properties of the generalized Gauss hypergeometric functions, Appl. Math. Inf. Sci. 2014; 8(5), 2315-2320.

P Agarwal. New unified integral involving a Srivastava polynomials and -function. J. Fract. Calc. Appl. 2012; 3, 1-7.

P Agarwal and S Jain. New integral formulas involving polynomials and I ̅-function. J. Appl. Math. Stat. Inform. 2012; 8, 79-88.

P Agarwal and S Jain. On unified finite integrals involving a multivariable polynomial and a generalized Mellin Barnes type of contour integral having general argument. Nat. Acad. Sci. Lett. 2009; 32, 281-6.

HM Srivastava. A multilinear generating function for the Konhauser sets of bi-orthogonal polynomials suggested by the Laguerre polynomials. Pacific J. Math. 1985; 117, 183-91.

VP Saxena. A formal solution of certain new pair of dual integral equations involving H-functions. Proc. Nat. Acad. Sci. India 1982; A52, 366-75.

HM Srivastava, KC Gupta and SP Goyal. The H-Function of One and Two Variables with Applications. South Asian Publishers, New Delhi, India, 1982.

VP Saxena. The I-Function. Anamaya Publishers, New Delhi, India, 2008.

IS Gradshteyan and IM Ryzhik. Tables of Integrals. Academic Press, New York, 1980.

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Published

2014-10-30

How to Cite

JAIN, S., & AGARWAL, P. (2014). A New Class of Integral Relations Involving General Class of Polynomials and I-Functions. Walailak Journal of Science and Technology (WJST), 12(11), 1009–1018. Retrieved from https://wjst.wu.ac.th/index.php/wjst/article/view/692