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1. Mittag-Leffler's polynomial gn(z) has the orthogonal property fgm(-ix)gn(ix)dx/xsh(x) = m $ n m > 0-co =-2/n m=n n>O. (1.1) This is readily obtained by inverting the integral representation' co gn(ix) = (1/ir) sin (irx)f exu (tanh '/2u)ndu/sh u n > 1 (1.2)-co0 by means of Fourier's inversion formula. The resulting equation co cosech u (tanh 1/2u)n = 1/2 e-iux cosech (irx)gn(ix)dx (1.3)-OD then gives the desired relation when sh u e-iux is expanded in powers of tanh 1/2u. With the notation of the hypergeometric function the orthogonal relation may be written in the form

An Orthogonal Property of the Hypergeometric Polynomial