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On the Application of a Hypergeometric Identity to Generate Generalized Hypergeometric Reduction Formulas [PDF]
AxiomsWe systematically exploit a new generalized hypergeometric identity to obtain new hypergeometric summation formulas. As a consistency test, alternative proofs for some special cases are also provided.
Juan Luis González-Santander
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A remarkable basic hypergeometric identity. [PDF]
Ramanujan JAbstract We give a closed form for quotients of truncated basic hypergeometric series where the base q is evaluated at roots of unity.
Krattenthaler C, Zudilin W.
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Some properties of generalized hypergeometric Appell polynomials [PDF]
Karpatsʹkì Matematičnì Publìkacìï, 2020 Let $x^{(n)}$ denotes the Pochhammer symbol (rising factorial) defined by the formulas $x^{(0)}=1$ and $x^{(n)}=x(x+1)(x+2)\cdots (x+n-1)$ for $n\geq 1$.
L. Bedratyuk, N. Luno
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Recurrent identities for two special functions of hypergeometric type
Вестник Самарского университета: Естественнонаучная серия, 2023 The article presents conclusions and proofs of Gauss-type identities for two known hypergeometric type functions. For the derivation and justification of formulas, the representation of functions in the form of a series is used, as well as an integral ...
Svetlana V. Podkletnova
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A note on a generalization of Riordan's combinatorial identity via a hypergeometric series approach [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this note, an attempt has been made to generalize the well-known and useful Riordan's combinatorial identity via a hypergeometric series approach.
Dongkyu Lim
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Applications of q-difference equation and homogeneous q-shift operator rΦs(Dxy) in q-polynomials
Partial Differential Equations in Applied Mathematics, 2023 In this paper, the generalized homogeneous q-shift operator is constructed. The q-difference equation is then utilized to construct numerous polynomial q-identities, such as the generating function and its extension, Rogers’ formula and its extension ...
Samaher A. Abdul-Ghani, Husam L. Saad
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A Note on Generalization of Combinatorial Identities Due to Gould and Touchard
Axioms, 2023 Using a hypergeometric series approach, a general combinatorial identity is found in this note, and among its special cases are well-known and classical combinatorial identities due to Gould and Touchard.
Arjun K. Rathie, Dongkyu Lim
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A General Family of q-Hypergeometric Polynomials and Associated Generating Functions
Mathematics, 2021 Basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and the basic (or q-) hypergeometric polynomials are studied extensively and widely due mainly to their potential for applications in many areas of ...
Hari Mohan Srivastava, Sama Arjika
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Bailey pairs for the q-hypergeometric integral pentagon identity
European Physical Journal C: Particles and Fields, 2023 In this work, we construct new Bailey pairs for the integral pentagon identity in terms of q-hypergeometric functions. The pentagon identity considered here represents the equality of the partition functions of certain three-dimensional supersymmetric ...
Ilmar Gahramanov, Osman Erkan Kaluc
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Mathematics, 2021 Integral inequalities for ℘-convex functions are established by using a generalised fractional integral operator based on Raina’s function. Hermite–Hadamard type inequality is presented for ℘-convex functions via generalised fractional integral operator.
Saima Rashid +3 more
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