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Everything about Polygamma function
Meromorphic function
In mathematics, the polygamma function of order m is a meromorphic function on the complex numbers defined as the (m + 1)th derivative of the logarithm of the gamma function: Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Polygamma functionA 5-minute orientation
- Skim a recent paper: Decreasing properties of two ratios defined by three and four polygamma functionsInfluential work since 2022
- Read the landmark paper: Polygamma functions of negative orderCited 55 times
- Go sideways: Digamma functionA closely related topic
- Go sideways: Rational zeta seriesA closely related topic
📖 Definitions
Noun A meromorphic function on ℂ, defined as the (m+1)-th derivative (for a given order m) of the logarithm of the gamma function.
🏆 Landmark papers (most cited)
Polygamma functions of negative order
Sharp inequalities for the digamma and polygamma functions
Complete monotonicity of some functions involving polygamma functions
On some properties of digamma and polygamma functions
Very accurate estimates of the polygamma functions
Inequalities for the Gamma and Polygamma Functions
Inequalities for the Polygamma Functions
Refinements of lower bounds for polygamma functions
🆕 Influential since 2022
Decreasing properties of two ratios defined by three and four polygamma functions
Several Functions Originating from Fisher–Rao Geometry of Dirichlet Distributions and Involving Polygamma Functions
Complete monotonicity involving the divided difference of polygamma functions
New summation formulas of Fox-Wright-type series containing the polygamma functions
A class of completely monotonic functions involving the polygamma functions
📚 Books worth reading
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🔗 Related topics
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