Abstract
By employing an interesting modification of the familiar multiplying-factor technique, which was developed elsewhere by B. Noble [Proc. Cambridge Philos. Soc. 59 , 363–371 (1963)], an exact solution is obtained for a certain pair of dual equations involving series of Jacobi polynomials. Also computed are the values of these general series on the intervals over which their values are not already specified. Several special or confluent cases of the dual series equations considered here are shown to lead to (known or new) dual equations involving series of Jacobi or Laguerre polynomials ; these simpler pairs of dual series equations were solved in the earlier works by A. P. Dwivedi and T. N. Trivedi [Indag. Math. 36 , 203–210 (1974)], J. S. Lowndes [Proc. Edinburgh Math. Soc. Ser. II 16 , 273–280 (1969)], Rekha Panda [Indag. Math. 39 , 122–127 (1977)], and H. M. Srivastava [ cf., e.g. , Indag. Math. 35 , 137–141 (1973)].
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