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Group Theoretic Origins of Certain Generating Functions of Legendre Polynomials

P. L. Rama Kameswari and V. S. Bhagavan

In this paper, Weisner’s group theoretic method is utilized to obtain the generating functions for the Legendre polynomials Pn (x). To derive the elements of Lie algebra, a suitable interpretation to the index n is given. Further, a linear independent differential operators was derived, which generates a Lie algebra. The principle interest in our results lies in the fact that, how the Weisner’s group-theoretic method can be applied suitably to the Legendre polynomials in order to derive six generating functions. Many results obtained are well known but some of them are believed to be new in the theory of special functions. Mathematics Subject Classification (2010): 33C10, 33C45, 33C50, 33C80.