The Fox-Wright function near the singularity and the branch cut

DOI10.1016/j.jmaa.2019.123664zbMath1433.30004arXiv1907.04597OpenAlexW2984222162WikidataQ126776596 ScholiaQ126776596MaRDI QIDQ2287265

Elena G. Prilepkina, Dmitriĭ Borisovich Karp

Publication date: 20 January 2020

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.04597

zbMATH Keywords

gamma functionasymptotic expansionFox-Wright functionFox's \(H\) functionNørlund-Bernoulli polynomial

Mathematics Subject Classification ID

Power series (including lacunary series) in one complex variable (30B10) Generalized hypergeometric series, ({}_pF_q) (33C20) Analytic continuation of functions of one complex variable (30B40)

Related Items (4)

Hypergeometric functions at unit argument: simple derivation of old and new identities ⋮ A catalogue of semigroup properties for integral operators with Fox–Wright kernel functions ⋮ Analytic normalized solutions of 2D fractional Saint-Venant equations of a complex variable ⋮ Unnamed Item

Cites Work

• Completely monotonic gamma ratio and infinitely divisible H-function of Fox
• Representations and inequalities for generalized hypergeometric functions
• A family of summation formulas on the Fox-Wright function
• Hypergeometric functions as generalized Stieltjes transforms
• Representations of hypergeometric functions for arbitrary parameter values and their use
• Asymptotical formulas for Gaussian and generalized hypergeometric functions
• Hypergeometric functions
• Exponentially small expansions in the asymptotics of the Wright function
• New integral representations for the Fox-Wright functions and its applications
• Reduction of a class of Fox-Wright Psi functions for certain rational parameters
• An inverse factorial series for a general gamma ratio and related properties of the Nørlund-Bernoulli polynomials
• Functional inequalities for the Fox-Wright functions
• Exponentially small expansions of the Wright function on the Stokes lines
• Some new facts concerning the delta neutral case of Fox's \(H\) function
• Sur les valeurs asymptotiques des nombres et des polynômes de Bernoulli
• The special functions and their approximations. Vol. I, II
• Contiguous relations for the Fox-Wright function
• The role of the Fox-Wright functions in fractional sub-diffusion of distributed order
• The Behavior of the Zero-Balanced Hypergeometric Series p F p-1 Near the Boundary of its Convergence Region
• Integration and Modern Analysis
• Singularity Analysis of Generating Functions
• Summation formulae on Fox–Wright Ψ-functions
• The Behavior at Unit Argument of the Hypergeometric Function ${}_3 F_2 $
• Generalized Hypergeometric Functions at Unit Argument
• Asymptotic expansions and inequalities for hypergeometric function
• Applications of the Stieltjes and Laplace transform representations of the hypergeometric functions
• Basic Theory
• Inequalities for Zero-Balanced Hypergeometric Functions
• Analytic Continuations of Higher-Order Hypergeometric Functions
• On some inequalities for the gamma and psi functions
• The Asymptotic Expansion of the Generalized Hypergeometric Function
• The Asymptotic Expansion of the Generalized Hypergeometric Function
• The role of Bell polynomials in integration
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