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Explicit evaluation of some families of log-sine integrals via the hypergeometric mechanism and their applications [PDF]
Notes on Number Theory and Discrete MathematicsIn this paper, we present explicit analytical expressions for certain families of log-sine definite integrals: ∫ₒ^2π xᵐ{ln(2sin(x/2))}ⁿdx (m∈ℕ₀, n∈ℕ), expressed in terms of multiple hypergeometric functions of the Kampe de Feriet with arguments ±1 and ...
Shakir Hussain Malik +1 more
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An Application of Subclasses of Harmonic Univalent Functions Involving Hypergeometric Function
Adıyaman University Journal of Science, 2020 The main purpose of this paper is to establish connections between various subclasses of harmonic univalent functions by applying certain convolution operator involving hypergeometric functions. We investigate such connections with Goodman- Salagean-Type harmonic univalent functions in the open unit disc U.
Yalçın Tokgöz, Sibel +2 more
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On extensions of two results due to Ramanujan [PDF]
, 2020 The aim in this note is to provide a generalization of an interesting entry in Ramanujan’s notebooks that relate sums involving the derivatives of a function φ(t) evaluated at 0 and 1.
Kim, Yong Sup +2 more
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Mathematics, 2022 The study done for obtaining the original results of this paper involves the fractional integral of the confluent hypergeometric function and presents its new applications for introducing a certain subclass of analytic functions. Conditions for functions
Alina Alb Lupaş, Georgia Irina Oros
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On the Properties of Special Functions on the linear-type lattices [PDF]
, 2011 We present a general theory for studying the difference analogues of special functions of hypergeometric type on the linear-type lattices, i.e., the solutions of the second order linear difference equation of hypergeometric type on a special kind of ...
Andrews +18 more
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On Complex Matrix-Variate Dirichlet Averages and Its Applications in Various Sub-Domains
Entropy, 2023 This paper is about Dirichlet averages in the matrix-variate case or averages of functions over the Dirichlet measure in the complex domain. The classical power mean contains the harmonic mean, arithmetic mean and geometric mean (Hardy, Littlewood and ...
Princy Thankamani +2 more
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مجلة العلوم البحتة والتطبيقية, 2020 The connection between different classes of special functions is a very important aspect in establishing new properties of the related classical functions that is they can inherit the properties of each other. Here we show how the Hermite polynomials are
Haniyah Saed Ben Hamdin
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Solving recurrences for Legendre–Bernstein basis transformations
Examples and Counterexamples, 2023 The change of basis matrix M from shifted Legendre to Bernstein polynomials and M−1 have applications in computer graphics. Algorithms use their properties to find the matrix elements efficiently.
D.A. Wolfram
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Fractal and Fractional, 2019 The main objective of this paper is to obtain certain new k-fractional estimates of Hermite−Hadamard type inequalities via s-convex functions of Breckner type essentially involving k-Appell’s hypergeometric functions.
Muhammad Uzair Awan +3 more
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Fractional parts of Linear polynomials and an application to hypergeometric functions [PDF]
Journal of the Australian Mathematical Society, 2001 AbstractUsing a result on arithmetic progressions, we describe a method for finding the rational h–tuples ρ = (ρl,…,ρh) such that all the multiples mρ (for m coprime to a denominator of ρ) lie in a linear variety modulo Z. We give an application to hypergeometric functions.
DVORNICICH, ROBERTO, ZANNIER U.
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