Results 31 to 40 of about 34,488 (206)
Hypergeometric Formulas for Lattice Sums and Mahler Measures [PDF]
, 2010 We prove a variety of explicit formulas relating special values of generalized hypergeometric functions to lattice sums with four indices of summation. These results are related to Boyd’s conjectured identities between Mahler measures and special values ...
Rogers, M.
core +2 more sources
Researches in MathematicsThis research article explores some new properties of generalized hypergeometric function and its q-analogue. The connections between ${}_{2}{{R}_{1}}^{\upsilon }(\mathfrak{z})$, the Wright function, and generalized Mittag-Leffler functions are explored.
K.K. Chaudhary, S.B. Rao
doaj +1 more source
Weighted hypergeometric functions and fractional derivative
Advances in Difference Equations, 2017 We introduce some weighted hypergeometric functions and the suitable generalization of the Caputo fractional derivation. For these hypergeometric functions, some linear and bilinear relations are obtained by means of the mentioned derivation operator ...
JE Restrepo +3 more
doaj +1 more source
Open Physics, 2022 The main aim of this article is to study a new generalizations of the Gauss hypergeometric matrix and confluent hypergeometric matrix functions by using two-parameter Mittag–Leffler matrix function.
Jain Shilpi +4 more
doaj +1 more source
Fractional operators with generalized Mittag-Leffler k-function
Advances in Difference Equations, 2019 In this paper, our main aim is to deal with two integral transforms involving the Gauss hypergeometric functions as their kernels. We prove some composition formulas for such generalized fractional integrals with Mittag-Leffler k-function.
Shahid Mubeen, Rana Safdar Ali
doaj +1 more source
Axioms, 2012 Recently, an extended operator of fractional derivative related to a generalized Beta function was used in order to obtain some generating relations involving the extended hypergeometric functions [1].
H. M. Srivastava +2 more
doaj +1 more source
A generalization of Clausen's identity
, 2009 The paper aims to generalize Clausen's identity to the square of any Gauss hypergeometric function. Accordingly, solutions of the related 3rd order linear differential equation are found in terms of certain bivariate series that can reduce to 3F2 series ...
G.E. Andrews +6 more
core +2 more sources
Machine Learning for Green Solvents: Assessment, Selection and Substitution
Advanced Science, EarlyView.Environmental regulations have intensified demand for green solvents, but discovery is limited by Solvent Selection Guides (SSGs) that quantify solvent sustainability. Training a machine learning model on GlaxoSmithKline SSG, a database of sustainability metrics for 10,189 solvents, GreenSolventDB is developed. Integrated with Hansen solubility metrics,
Rohan Datta +4 more
wiley +1 more source
Generalized hypergeometric functions at unit argument [PDF]
Proceedings of the American Mathematical Society, 1992 The analytic continuation near z = 1 z = 1 of the hypergeometric function p + 1 F p ( z ) _{p + 1}{F_p}\left ( z \right ) is ...
openaire +3 more sources
Symmetry, 2022 There have been numerous investigations on the hypergeometric series 2F1 and the generalized hypergeometric series pFq such as differential equations, integral representations, analytic continuations, asymptotic expansions, reduction cases, extensions of one and several variables, continued fractions, Riemann’s equation, group of the hypergeometric ...
Mohd Idris Qureshi +2 more
openaire +1 more source