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Everything about Reciprocal gamma function
Mathematical function
In mathematics, the reciprocal gamma function is the function where Γ(z) denotes the gamma function. Since the gamma function is meromorphic and nonzero everywhere in the complex plane, its reciprocal is an entire function. As an entire function, it is of order 1 (meaning that log log |1/Γ(z)| grows no faster than log |z|), but of infinite type (meaning that log |1/Γ(z)| grows faster than any multiple of |z|, since its growth is approximately proportional to |z| log |z| in the left-half plane). Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Reciprocal gamma functionA 5-minute orientation
- Skim a recent paper: Logarithmically absolute monotonicity of the ratio between normalized remainders for a function in an integral representation of the reciprocal of the gamma functionInfluential work since 2022
- Pick up a classic book: The Genius of EulerThe most-reprinted book on the subject
- Read the landmark paper: Log-concavity for series in reciprocal gamma functions and applicationsCited 23 times
- Go sideways: Gamma functionA closely related topic
- Go sideways: Polygamma functionA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Log-concavity for series in reciprocal gamma functions and applications
Regularized Integral Representations of the Reciprocal Gamma Function
Error bounds and exponential improvements for the asymptotic expansions of the gamma function and its reciprocal
On Data Augmentation for Models Involving Reciprocal Gamma Functions
Asymptotic expansions for the reciprocal of the gamma function
Polynomials orthogonal with respect to the reciprocal gamma function
Calculation of the Moments and the Moment Generating Function for the Reciprocal Gamma Distribution
Calculation of the moments and the moment generating function for the reciprocal gamma distribution
🆕 Influential since 2022
Logarithmically absolute monotonicity of the ratio between normalized remainders for a function in an integral representation of the reciprocal of the gamma function
Some properties of normalized remainders of the Maclaurin expansion for a function originating from an integral representation of the reciprocal of the gamma function
INTEGRAL-BASED FORMULATION INVOLVING THE RECIPROCAL GAMMA FUNCTION
Geometric Properties of Derivative of Reciprocal of Gamma Function and its Barnes G-analogue
Subclass of uniformly starlike functions associated with a linear operator whose coefficients are the reciprocal Gamma function
📚 Books worth reading
The Genius of EulerWilliam Dunham · 2007- 📕Table of the reciprocal of the gamma function for complex argumentJ. P. Stanley · 1950
- 📕Table of the reciprocal of the gamma function for complex argumentJ P. Stanley · 1950
- 📕Table of the reciprocal of the gamma function for complex argumentJohn Pearson Stanley · 1950
Mathematical Techniques in Chrystallography and Materials ScienceEdward Prince · 2004
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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