RACSAM DOI 10.1007/s13398-016-0343-x ORIGINAL PAPER Certain properties of Gegenbauer polynomials via Lie algebra Jyotindra C. Prajapati 1 · Junesang Choi 2 · Krunal B. Kachhia 3 · Praveen Agarwal 4 Received: 11 February 2016 / Accepted: 1 October 2016 © Springer-Verlag Italia 2016 Abstract We establish a result for the product of two operators defined on a Lie algebra of endomorphisms of a vector space. Then we use this result to derive some properties for Gegenbauer polynomials, for example, Rodrigues formula. The method developed here is potentially useful to investigate some other special functions of mathematical physics. Keywords Lie algebra · Endomorphism · Gegenbauer polynomials · Legendre polynomials · Rodrigues formula Mathematics Subject Classification Primary 33C45; Secondary 33C50 · 33C80 Contents 1 Introduction ................................................ 2 Main result ................................................. 3 A concrete application ........................................... B Junesang Choi junesang@mail.dongguk.ac.kr Jyotindra C. Prajapati jyotindra18@rediffmail.com Krunal B. Kachhia krunalmaths@hotmail.com Praveen Agarwal goyal.praveen2011@gmail.com 1 Department of Mathematics, Faculty of Technology and Engineering, Marwadi Education Foundation Group of Institutions (MEFGI), Rajkot 360003, Gujarat, India 2 Department of Mathematics, Dongguk University, Gyeongju 38066, Republic of Korea 3 Department of Mathematical Sciences, Faculty of Applied Sciences, Charotar University of Science and Technology (Charusat), Changa, Anand 388421, Gujarat, India 4 Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India