In this paper, by introducing two sequences of new numbers and their derivatives, which are closely related to the Stirling numbers of the first kind, and choosing to employ six known generalized Kummer’s summation formulas for 2F1(−1) and 2F1(1/2), we establish six classes of generalized summation formulas for p+2Fp+1 with arguments −1 and 1/2 for any positive integer p. Next, by differentiating both sides of six chosen formulas presented here with respect to a specific parameter, among numerous ones, we demonstrate six identities in connection with finite sums of 4F3(−1) and 4F3(1/2). Further, we choose to give simple particular identities of some formulas presented here. We conclude this paper by highlighting a potential use of the newly presented numbers and posing some problems.

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In this article, we aim at obtaining the analytical expression (not previously found and recorded in the literature) for the exact curved surface area of a hyperboloid of one sheet in terms of Srivastava-Daoust triple hypergeometric function. The derivation is based on Mellin-Barnes type contour integral representations of generalized hypergeometric function p F q (z), Meijer's G-function, decomposition formula for Meijer's G-function and series rearrangement technique. Further, we also obtain the formula for the volume of a hyperboloid of one sheet. The closed forms for the exact curved surface area and volume of the hyperboloid of one sheet are also verified numerically by using Mathematica Program.

In this article we aim at obtaining the semi-differentials of Complete Elliptic integrals of different kinds and their differences in terms of algebraic functions by using series manipulation technique and Pfaff-Kummer linear ¨ transformation.

Rao and Rao[16] obtained a triple fixed point theorem for a multimap in Hausdorff fuzzy metric space. Extending this idea we generalize the concept of triple fixed point, we define quadruple fixed point. In this paper we have established a result regarding it in Hausdorff fuzzy metric space. 2010 Mathematics Subject Classifications: 47H10, 54H25