IT is indeed curious that, after a lapse of nearly forty years, during which the tables of Tallqwist, first published at Helsingfors in 1906, have remained the only example of tabulation of the ...

Legendre polynomials are the most familiar orthogonal polynomials, and are used in approximation theory. Their generalizations, called Legendre functions, are parametrized by an order as well as a ...

PNAS is the world's most-cited multidisciplinary scientific serial. It publishes high-impact research reports, commentaries, perspectives, reviews, colloquium papers, and actions of the Academy. In ...

Let $P^m_{-1/2 + i_x}(z)$ be the associated Legendre function of order $m$ and degree $-1/2 + ix$. We give, here, two integral transforms $G^m$ and $H^m$, arising ...