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Results for "digamma"

Dilogarithm

Definition: The term "dilogarithm" is a mathematical function in complex analysis and number theory, specifically used in the study of the logarithmic derivative. It was introduced by the German mathematician August Ferdinand Liouville around 1860, who called it a "logarithm to the second power." The dilogarithm is closely related to the concept of the digamma function, which is used in mathematical analysis and complex analysis to study the behavior of certain functions.


dilogarithm

Digammic

Definition: The term "digamma" is derived from Greek and refers to a specific function in mathematical analysis, particularly for complex numbers. Specifically, it is defined as: $$ \psi(z) = \sum_{n=0}^{\infty} \frac{z^n}{n!} $$ This function is often used in probability theory, especially in the study of random variables and the gamma distribution. In other words, digamma functions are a special case of the gamma function, which


digammic

Digammated

Definition: The term "digamma function" is derived from the Greek word "digama," which means "infinite." The digamma function, denoted by $\psi(x)$ or $\psi(x)^\prime$, is defined as: $$\psi(x) = \frac{1}{x} + \sum_{n=2}^{\infty}\left(\frac{x}{n}-\frac{1}{(n+1)x}\right)\tag{1}$$


digammated

Digammate

Definition: In mathematics, a digamma function is defined as: φ(z) = ∫_0^∞ (z - x)^(-1) e^{-x} dx This function is named after the Greek letter gamma (Γ), which represents the gamma function. The digamma function is important in the study of complex analysis and has applications in various fields such as number theory, probability theory, and mathematical physics.


digammate

Digammas

Definition: In linguistics, a digamma (represented as Γε) is an irrational number that is defined by the equation: Γε = Σ n=1 ∞ (1/2^n - 1/3^n) Where n is a natural number. This definition allows us to express the sum of reciprocals of consecutive integers in terms of an infinite series. It's often used in mathematics, statistics, and probability theory to model natural phenomena like the growth rate of populations over time


digammas

Digamma

Definition: The term "digamma" is derived from Greek and refers to a function in complex analysis. In mathematics, it is used to study the behavior of certain functions known as meromorphic functions. Specifically, digammas are defined for holomorphic functions on the unit disk (the set of all complex numbers with absolute value less than 1) which satisfy certain conditions. The digamma function, denoted by ψ(z), is a generalized gamma function defined for complex z and its domain includes the


digamma