CERTAIN QUADRUPLE SERIES EQUATIONS INVOLVING LAGUERRE POLYNOMIALS

By

Omkar Lal Shrivastava ¹ and Kuldeep Narain ²

¹Department of Mathematics

Government Kamladevi Rathi Girls Postgraduate College, Rajnandgaon-491441, Chhattisgarh, India

Email: omkarlal@gmail.com

²Department of Mathematics

Kymore Science College, Kymore-483880, Madhya Pradesh, India

Email: kuldeepnarain2009@gmail.com

(Received : November 30, 2020 ; Revised: December 24, 2020)

Srivastava ([13], [15]) has solved dual series equations involving Bateman-k functions and Jacobi polynomials. Srivastava [16] has obtained more results for the Konhauser-biorhogonal set. Lowndes ([3], [4]), Srivastava [12], Lowndes and Srivastava [5], Srivastava[14], Srivastava and Panda [17] have obtained the solution of dual series equations involving Jacobi and Laguerre polynomials and also solved triple series equations involving Laguerre polynomials. Singh, Rokne and Dhaliwal [10] have find out the solution of triple series equations involving Laguerre polynomials in a closed form. Kuldeep Narain ([7], [8]), Rajnesh Krishnan Mudaliar and Kuldeep Narain [6] have solved Certain dual and quadruple series equations involving generalized Laguerre polynomials and Jacobi polynomials as kernels. In the present paper, an exact solution has been obtained for the quadruple series equations involving Laguerre polynomials by Noble [9] modified multiplying factor technique.

2010 Mathematics Subject Classifications: 45XX, 33C45, 33D45, 34BXX

Keywords and phrases: Laguerre polynomials, Basic orthogonal polynomials and functions, Boundary value problems.