Certain Series of Basic Bessel Coefficients

Linearization coefficients of Bessel polynomials

We prove positivity results about linearization and connection coefficients for Bessel polynomials. The proof is based on a recursion formula and explicit formulas for the coefficients in special cases. The result implies that the distribution of a convex combination of independent Studentt random variables with arbitrary odd degrees of freedom has a density which is a convex combination of cer...

On Certain Series Involving Reciprocals of Binomial Coefficients

We evaluate the following family of series involving reciprocals of binomial coefficients in terms of elementary functions for m = 3,4. ∞ ∑ k=0 xk (mk+1) (mk k ) .

Certain Aspects of Univalent Function with Negative Coefficients Defined by Bessel Function

Certain Estimates for Double Sine Series with Multiple-monotone Coefficients

Formulas of Ramanujan for the Power Series Coefficients of Certain Quotients of Eisenstein Series

In their last published paper [9], [16, pp. 310–321], G. H. Hardy and S. Ramanujan derived infinite series representations for the coefficients of certain modular forms of negative weight which are not analytic in the upper half-plane. In particular, they examined in detail the coefficients of the reciprocal of the Eisenstein series E6(τ). While confined to the sanitarium, Matlock House, in 191...