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Everything about Digamma function
Mathematical function
In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function: Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Digamma functionA 5-minute orientation
- Skim a recent paper: FUNCTIONAL INEQUALITIES FOR THE q-DIGAMMA FUNCTIONInfluential work since 2022
- Pick up a classic book: Tables of the digamma and trigamma functionsThe most-reprinted book on the subject
- Read the landmark paper: Algorithm AS 103: Psi (Digamma) FunctionCited 95 times
- Go sideways: Polygamma functionA closely related topic
- Go sideways: Stieltjes constantsA closely related topic
📖 Definitions
Noun The first of the polygamma functions, being the logarithmic derivative of the gamma function.
🗂️ The subject at a glance
- Relation to harmonic numbers
- Integral representations
- Infinite product representation
- Series representation
- Reflection formula
- Recurrence formula and characterization
- Some finite sums involving the digamma function
- Gauss's digamma theorem
- Multiplication theorem
- Asymptotic expansion
- Inequalities
- Computation and approximation
🏆 Landmark papers (most cited)
Algorithm AS 103: Psi (Digamma) Function
New approximations of the gamma function in terms of the digamma function
Summations for basic hypergeometric series involving a q-analogue of the digamma function
Transcendental values of the digamma function
Asymptotic formulae associated with the Wallis power function and digamma function
Convexity, Schur-Convexity and Bounds for the Gamma Function Involving the Digamma Function
Summations for certain series containing the digamma function
Infinite family of approximations of the Digamma function
🆕 Influential since 2022
FUNCTIONAL INEQUALITIES FOR THE q-DIGAMMA FUNCTION
Sums Involving the Digamma Function Connected to the Incomplete Beta Function and the Bessel functions
Around the Gauss theorem on the values of Euler’s digamma function at rational points
Fractional Hermite–Hadamard-Type Inequalities for Differentiable Preinvex Mappings and Applications to Modified Bessel and q-Digamma Functions
Finite and Infinite Hypergeometric Sums Involving the Digamma Function
📚 Books worth reading
Tables of the digamma and trigamma functionsEleanor Pairman · 1919
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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