Topic
Gamma function
About: Gamma function is a research topic. Over the lifetime, 1849 publications have been published within this topic receiving 29146 citations. The topic is also known as: complete gamma function.
Papers published on a yearly basis
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Papers
TL;DR: All real numbers α = α( p) and β = β(p) such that the inequalities formula math.
Abstract: Let p ¬= 1 be a positive real number. We determine all real numbers α = α(p) and β = β(p) such that the inequalities formula math. formula math. are valid for all x > 0. And, we determine all real numbers a and b such that - log(1 - e -ax ) ≤ √ x ∞ e-t/t ≤ - log(1 - e -bx ) hold for all > 0.
436 citations
419 citations
TL;DR: In this article, the Laplace transform for the nabla derivative on the time scale of integers is introduced and properties of discrete fractional calculus in the sense of a backward difference are introduced and developed.
Abstract: Properties of discrete fractional calculus in the sense of a backward difference are introduced and developed. Exponential laws and a product rule are developed and relations to the forward fractional calculus are explored. Properties of the Laplace transform for the nabla derivative on the time scale of integers are developed and a fractional finite difference equation is solved with a transform method. As a corollary, two new identities for the gamma function are exhibited.
410 citations
1 Jan 1996
TL;DR: The machinery of power series for representing functions and solving various problems of mathematics and mechanics was used systematically by Newton starting in the l660s as discussed by the authors and it was left to the eighteenth century to perfect the technique of operating with power series, the series used by Newton being supplemented by the series of Taylor and Lagrange.
Abstract: The machinery of power series for representing functions and solving various problems of mathematics and mechanics was used systematically by Newton starting in the l660’s. However it was left to the eighteenth century to perfect the technique of operating with power series, the series used by Newton being supplemented by the series of Taylor and Lagrange. In the eighteenth century, mostly at the initiative of Euler. infinite products, partial fraction expansions, integral representations (gamma function, elliptic integrals), and continued fractions were applied along with power series.
392 citations
TL;DR: In this article, a generalization of the exponential function exp ( z ) was introduced and its properties including usual differentiation and integration, Laplace transforms, Euler (Beta) transforms, Mellin transforms, Whittaker transforms, generalised hypergeometric series form and Mellin-Barnes integral representation with their several special cases are obtained and its relationship with Laguerre polynomials, Fox H-function and Wright hypergeometry function is also established.
391 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 10 |
| 2024 | 19 |
| 2023 | 60 |
| 2022 | 48 |
| 2021 | 96 |
| 2020 | 82 |