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THE PRODUCT OF GENERALIZED POLYNOMIALS SETS PERTAINING TO A CLASS OF CONVOLUTION INTEGRAL EQUATIONS

THE PRODUCT OF GENERALIZED POLYNOMIALS SETS PERTAINING TO A CLASS OF CONVOLUTION INTEGRAL EQUATIONS D E M O N S T R A T E MATHEMATICAVol. XLIINo 32009V. B. L. Chaurasia, Mukesh AgnihotriTHE PRODUCT OF GENERALIZED POLYNOMIALS SETSPERTAINING TO A CLASS OF CONVOLUTIONINTEGRAL EQUATIONSA b s t r a c t . The purpose of this paper is to obtain a certain class of convolution integralequation of Fredholm type with the product of two generalized polynomials sets. Usingof the Mellin transform technique; we have established solution of the integral equation.1. IntroductionThe polynomial setR%b[x](1.1)c, d, n,«/; «,(*)]a , ¡3,7,(axcis introduced by Agrawal and Chaubey [2].+ P)~a{ -yxd + S) - o=(axcKnw(x)+ (3)a+»n(7xd+ S)b+vnw(x),n = 0 , 1 , 2 , . . . , where(1.2)Ti;i =+xDx),Dx=7, S, a, b, c, d, n, v are constants, {Kn}^L0is a sequence of constants, andw(x) is any general function of x, differentiate an arbitrary number of times.The polynomial set R%b[x] is general in nature and gets a number ofknown polynomials as its special cases.If, we take c = d = 1, Kn = n!, <; = 0, n = —1, the polynomial setR%b[x] reduces to Sn'b[x,a,(3,^,6;,n,v,w(x)],it is defined by Srivastavaand Panda [6].a, ¡3,In this paper, we shall investigate the inversion of the integral(1.3)n *<*)= n¿=1,2¿=1,2 0T f c http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

THE PRODUCT OF GENERALIZED POLYNOMIALS SETS PERTAINING TO A CLASS OF CONVOLUTION INTEGRAL EQUATIONS

Chaurasia, V. B. L.; Agnihotri, Mukesh
Demonstratio Mathematica , Volume 42 (3): 8 – Jul 1, 2009
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Publisher
de Gruyter
Copyright
© by V. B. L. Chaurasia
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2009-0306
Publisher site
See Article on Publisher Site

Abstract

D E M O N S T R A T E MATHEMATICAVol. XLIINo 32009V. B. L. Chaurasia, Mukesh AgnihotriTHE PRODUCT OF GENERALIZED POLYNOMIALS SETSPERTAINING TO A CLASS OF CONVOLUTIONINTEGRAL EQUATIONSA b s t r a c t . The purpose of this paper is to obtain a certain class of convolution integralequation of Fredholm type with the product of two generalized polynomials sets. Usingof the Mellin transform technique; we have established solution of the integral equation.1. IntroductionThe polynomial setR%b[x](1.1)c, d, n,«/; «,(*)]a , ¡3,7,(axcis introduced by Agrawal and Chaubey [2].+ P)~a{ -yxd + S) - o=(axcKnw(x)+ (3)a+»n(7xd+ S)b+vnw(x),n = 0 , 1 , 2 , . . . , where(1.2)Ti;i =+xDx),Dx=7, S, a, b, c, d, n, v are constants, {Kn}^L0is a sequence of constants, andw(x) is any general function of x, differentiate an arbitrary number of times.The polynomial set R%b[x] is general in nature and gets a number ofknown polynomials as its special cases.If, we take c = d = 1, Kn = n!, <; = 0, n = —1, the polynomial setR%b[x] reduces to Sn'b[x,a,(3,^,6;,n,v,w(x)],it is defined by Srivastavaand Panda [6].a, ¡3,In this paper, we shall investigate the inversion of the integral(1.3)n *<*)= n¿=1,2¿=1,2 0T f c

Journal

Demonstratio Mathematica – de Gruyter

Published: Jul 1, 2009

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