In this article, by making use of a q-analogue the familiar Borel distribution, we introduce two new subclasses: S?,?,q symmetric(b, A, B) and conjugate(b,A, starlike convex functions in open unit disk ? with respect to symmetric conjugate points. We obtain some properties including Taylor-Maclaurin coefficient estimates for each these subclasses deduce various corollaries consequences main res...

Efficient recurrence relations for computing arbitrary-order Taylor coefficients for any univariate function can be directly applied to a function of n variables by fixing a direction in Rn. After a sequence of directions, the multivariate Taylor coefficients or partial derivatives can be reconstructed or “interpolated”. The sequence of univariate calculations is more efficient than multivariat...

Hirschman and Widder introduced a class of Pólya frequency functions given by linear combinations one-sided exponential functions. The members this are probability densities, the is closed under convolution but not pointwise multiplication. We show that, generically, polynomial function such density only if homothety, also identify subclass for which each positive-integer power function. furthe...

It is by now well understood that, for functions defined by computer programs Taylor, polynomials in several variables can be recovered from families of univariate polynomials. We observe here that by adapting an idea of Kronecker it is possible to get by with a single univariate polynomial of rather high order. Hence the evaluation of higher derivatives can be based on the propagation of univa...