The Journal of the Indian Mathematical Society

M. Bhimasena Rao , M. Venkatarama Iyer

Abstract

Let     F ( z , n )= ∫ ^∞ ₀ e^-xz M_x (x) dx,

where the function M_x(x)* is such that the above integral is convergent and that as x ⃗ ∞, M_x (x) e ^-xz ⃗ 0, for all integral values of n ≥ 1 (a condition satisfied in the case of the several functions which were obtained as particular cases of the general M -function).

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M. Bhimasena Rao , M. Venkatarama Iyer

Abstract

In a paper on ' Determinants involving specified numbers,' three persymmetric determinants whose elements are integrals of Legendre's Polynomials were taken and their values given without proof.† In this paper, the missing proof and a general mode of evaluation are supplied along with a few more new results.

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