Função digama

Função digama no plano complexo. A cor de um ponto representa o valor de . Cores fortes representam valores próximos de zero e matizes representam os valores de argumento.

Em matemática, as funções poligama são definidas como a n-ésima derivada da função psi, que é a derivada logarítmica da função gama:[1]

A função digama também é chamada de função Psi.[2]

Relação com os números harmônicos

A função digama está relacionada com os números harmônicos por:

em que γ é a constante de Euler-Mascheroni. Para valores semi-inteiros, os valores da função digama são:

Referências

  1. ↑ GNU Scientific Library, Reference Manual, 7.28 Psi (Digamma) Function [em linha]
  2. ↑ GNU Scientific Library, Reference Manual, 7.28.1 Digamma Function [em linha]

Bibliografia

  • Abramowitz, M. and Stegun, I. A. (Eds.). "Psi (Digamma) Function." §6.3 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 258–259, 1972. Ver seção §6.4

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