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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