An application of theory of distributions to the family of \(\lambda \)-generalized gamma function

DOI10.3934/math.2020374zbMath1484.33006OpenAlexW3043144248MaRDI QIDQ2132149

Asifa Tassaddiq

Publication date: 27 April 2022

Published in: AIMS Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/math.2020374

zbMATH Keywords

Fourier transformationdelta function\( \lambda \)-generalized gamma functiongeneralized functions (distributions)slowly increasing test functions

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Topological linear spaces of test functions, distributions and ultradistributions (46F05)

Related Items (2)

Unified approach to fractional calculus images involving the pathway transform of extended \(k\)-gamma function and applications ⋮ On modifications of the gamma function by using Mittag-Leffler function

Uses Software

• DLMF

Cites Work

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• Fourier transform and distributional representation of the generalized gamma function with some applications
• Two-sided inequalities for the extended Hurwitz-Lerch zeta function
• Some further properties of a linear operator associated with the \(\lambda\)-generalized Hurwitz-Lerch zeta function related to the class of meromorphically univalent functions
• Fourier transform representation of the generalized hypergeometric functions with applications to the confluent and Gauss hypergeometric functions
• A comparison theorem for two divided differences and applications to special functions
• Fourier transform and distributional representation of the gamma function leading to some new identities
• On complete monotonicity for several classes of functions related to ratios of gamma functions
• Sharp bounds for the ratio of two zeta functions
• Asymptotic expansions for the gamma function in terms of hyperbolic functions
• A new integral transform associated with the \(\lambda \)-extended Hurwitz-Lerch zeta function
• New expansion formulas for a family of the \(\lambda\)-generalized Hurwitz-Lerch zeta functions
• Monotonicity, convexity, and complete monotonicity of two functions related to the gamma function
• Some difference equations for Srivastava's \({\lambda}\)-generalized Hurwitz-Lerch zeta functions with applications
• A new representation for Srivastava's \(\lambda\)-generalized Hurwitz-Lerch zeta functions
• On rational bounds for the gamma function
• Fourier transform representation of the extended Fermi–Dirac and Bose–Einstein functions with applications to the family of the zeta and related functions
• Integral and computational representations of the extended Hurwitz–Lerch zeta function
• Sharp Gautschi inequality for parameter 0<p<1 with applications
• On approximating the error function
• A class of completely mixed monotonic functions involving the gamma function with applications
• New results for Srivastava’s λ-generalized Hurwitz-Lerch Zeta function
• A new asymptotic expansion of a ratio of two gamma functions and complete monotonicity for its remainder
• Certain subclasses of meromorphically univalent functions defined by a linear operator associated with theλ-generalized Hurwitz–Lerch zeta function

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