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mathematical physics > special function > polygamma function of order m > digamma function

mathematical analysis > functional analysis > special function > polygamma function of order m > digamma function

mathematical analysis > complex analysis > meromorphic function > polygamma function of order m > digamma function

Preferred term

digamma function

In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function:
${\\displaystyle \\psi (z)={\ rac {\\mathrm {d} }{\\mathrm {d} z}}\\ln \\Gamma (z)={\ rac {\\Gamma '(z)}{\\Gamma (z)}}.}$
It is the first of the polygamma functions. This function is strictly increasing and strictly concave on ${\\displaystyle (0,\\infty )}$ , and it asymptotically behaves as
${\\displaystyle \\psi (z)\\sim \\ln {z}-{\ rac {1}{2z}},}$
for large arguments ( ${\\displaystyle |z|\ ightarrow \\infty }$ ) in the sector ${\\displaystyle |\\arg z|<\\pi -\\varepsilon }$ with some infinitesimally small positive constant ${\\displaystyle \\varepsilon }$ . The digamma function is often denoted as ${\\displaystyle \\psi _{0}(x),\\psi ^{(0)}(x)}$ or $Ϝ$ (the uppercase form of the archaic Greek consonant digamma meaning double-gamma).
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Digamma_function)

polygamma function of order m

fonction digamma

French

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http://data.loterre.fr/ark:/67375/PSR-HKKTJN0R-G

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