Opened 7 years ago

# expansion of psi(m/n)

Reported by: Owned by: rws minor sage-wishlist symbolics special, psi, polygamma, expansion N/A

### Description

As example, expressions with several psi values of rational argument result from infinite sums:

```sage: sum((-1)^(k+1)/(4*k-3), k, 1, oo)
1/8*psi(5/8) - 1/8*psi(1/8)
```

`psi(m/n)`, m<k, has a closed form of finitely many terms of elementary functions, so differences of psi values can yield nice expressions like `1/8*psi(5/8) - 1/8*psi(1/8) = 1/(4*sqrt(2))*(pi+2*log(sqrt(2)+1))`

To arrive at such simplifications the expansion of `psi(m/n)` using Gauss' Digamma Theorem should be implemented.

### comment:1 Changed 7 years ago by rws

• Keywords polygamma added; digamma removed
• Priority changed from major to minor

### comment:2 Changed 7 years ago by vbraun_spam

• Milestone changed from sage-6.3 to sage-6.4

### comment:3 Changed 6 years ago by rws

• Milestone changed from sage-6.4 to sage-wishlist
Note: See TracTickets for help on using tickets.