CERTAIN QUADRUPLE SERIES EQUATIONS INVOLVING LAGUERRE POLYNOMIALS
Omkar Lal Shrivastava 1 and Kuldeep Narain 2
1Department of Mathematics
Government Kamladevi Rathi Girls Postgraduate College, Rajnandgaon-491441, Chhattisgarh, India
2Department of Mathematics
Kymore Science College, Kymore-483880, Madhya Pradesh, India
(Received : November 30, 2020 ; Revised: December 24, 2020)
Srivastava (, ) has solved dual series equations involving Bateman-k functions and Jacobi polynomials. Srivastava  has obtained more results for the Konhauser-biorhogonal set. Lowndes (, ), Srivastava , Lowndes and Srivastava , Srivastava, Srivastava and Panda  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  have find out the solution of triple series equations involving Laguerre polynomials in a closed form. Kuldeep Narain (, ), Rajnesh Krishnan Mudaliar and Kuldeep Narain  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  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.
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