, 55:41 | Cite as

Biorthogonality and para-orthogonality of \(R_I\) polynomials

  • Kiran Kumar Behera
  • A. SwaminathanEmail author


In this paper, a sequence of linear combination of \(R_{I}\) polynomials such that the terms in this sequence have a common zero is constructed. A biorthogonality relation arising from such a sequence is discussed. Besides, a sequence of para-orthogonal polynomials by removing the common zero using suitable conditions is obtained. Finally, a case of hypergeometric functions is studied with numerical observations to illustrate the results obtained.


\(R_{I}\) recurrence relations Linear combinations of polynomials Biorthogonality Para-orthogonal polynomials 

Mathematics Subject Classification

Primary 42C05 15A18 33C45 



The authors wish to thank the anonymous referees for their constructive criticism of the work which has helped in removing many ambiguities in the text and in particular for the numerical part in Sect. 5.


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Copyright information

© Istituto di Informatica e Telematica del Consiglio Nazionale delle Ricerche 2018

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology, RoorkeeRoorkeeIndia

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