@prefix psr: . @prefix skos: . @prefix dc: . @prefix xsd: . psr: a skos:ConceptScheme . psr:-QK86QW05-V skos:prefLabel "polygamma function of order m"@en, "fonction polygamma d'ordre m"@fr ; a skos:Concept ; skos:narrower psr:-HKKTJN0R-G . psr:-HKKTJN0R-G dc:modified "2024-10-18"^^xsd:date ; skos:definition """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)}

Ϝ

(the uppercase form of the archaic Greek consonant digamma meaning double-gamma).
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Digamma_function)"""@en, """En mathématiques, la fonction digamma ou fonction psi est définie comme la dérivée logarithmique de la fonction gamma :

{\\\\displaystyle \\\\psi (z)={\\ rac {\\\\Gamma '(z)}{\\\\Gamma (z)}}.}

(Wikipedia, L'Encylopédie Libre, https://fr.wikipedia.org/wiki/Fonction_digamma)"""@fr ; skos:prefLabel "digamma function"@en, "fonction digamma"@fr ; a skos:Concept ; skos:exactMatch , ; skos:inScheme psr: ; skos:broader psr:-QK86QW05-V .