Digamma Function/Examples/Digamma Function of Two
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Example of Use of Recurrence Relation for Digamma Function
- $\map \psi 2 = -\gamma + 1$
Proof
| \(\ds \map \psi {z + 1}\) | \(=\) | \(\ds \map \psi z + \frac 1 z\) | Recurrence Relation for Digamma Function | |||||||||||
| \(\ds \leadsto \ \ \) | \(\ds \map \psi {1 + 1}\) | \(=\) | \(\ds \map \psi 1 + 1\) | $z := 1$ | ||||||||||
| \(\ds \leadsto \ \ \) | \(\ds \map \psi 2\) | \(=\) | \(\ds -\gamma + 1\) | Digamma Function of One |
$\blacksquare$