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Applications of integral transforms in generating summable series involving higher transcendental functions Public Deposited

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  • A large number of results concerning the sums of certain infinite series involving Legendre functions (including conical functions) are derived. The generating principle chosen here is based upon the application of Integral transforms of the Fourier, Hankel and Meijer type of finite and infinite character. This particular choice leads to a group of three different types of Legendre series: Fourier series type, Cardinal series type and addition theorem type. The presented material is believed to be new and reduces, upon specialization of certain parameters, in a number of cases to already known relations. In view of the scope of the results, it seemed best to give their derivation in a rather condensed form; and for the sake of conciseness, frequently using tables as a method of arrangement. A list of notations and definitions of the occuring functions is given in an appendix.
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