Digamma function: Difference between revisions

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:<math>\psi(z) \sim \ln{z} - \frac{1}{2z},</math>
 
for complex numbers with large modulus (<math>|z|\rightarrow\infty</math>) in the [[Circular sector|sector]] <math>|\arg z|<\pi-\varepsilon</math> withfor some [[Infinitesimal|infinitesimally small]] positive constantany <math>\varepsilon > 0</math>.
 
The digamma function is often denoted as <math>\psi_0(x), \psi^{(0)}(x) </math> or {{math|Ϝ}}<ref>{{cite book |last=Pairman |first=Eleanor |author-link=Eleanor Pairman |date=1919 |title=Tables of the Digamma and Trigamma Functions |url=https://archive.org/details/cu31924001468416/page/n9/mode/2up |publisher=Cambridge University Press |page=5}}</ref> (the uppercase form of the archaic Greek [[consonant]] [[digamma]] meaning [[Gamma|double-gamma]]).