[mpmath] r1239 committed - enable zeta/polylog reduction in lerchphi

[mpm...@googlecode.com]

Revision: 1239
Author: fredrik.johansson
Date: Fri Jul 22 02:14:49 2011
Log: enable zeta/polylog reduction in lerchphi
http://code.google.com/p/mpmath/source/detail?r=1239

Modified:
/trunk/mpmath/functions/zeta.py

=======================================
--- /trunk/mpmath/functions/zeta.py Fri Jan 28 12:37:56 2011
+++ /trunk/mpmath/functions/zeta.py Fri Jul 22 02:14:49 2011
@@ -1110,6 +1110,21 @@
>>> lerchphi(0,1,-2)
-0.5

+ Reduction to simpler functions::
+
+ >>> lerchphi(1, 4.25+1j, 1)
+ (1.044674457556746668033975 - 0.04674508654012658932271226j)
+ >>> zeta(4.25+1j)
+ (1.044674457556746668033975 - 0.04674508654012658932271226j)
+ >>> lerchphi(1 - 0.5**10, 4.25+1j, 1)
+ (1.044629338021507546737197 - 0.04667768813963388181708101j)
+ >>> lerchphi(3, 4, 1)
+ (1.249503297023366545192592 - 0.2314252413375664776474462j)
+ >>> polylog(4, 3) / 3
+ (1.249503297023366545192592 - 0.2314252413375664776474462j)
+ >>> lerchphi(3, 4, 1 - 0.5**10)
+ (1.253978063946663945672674 + 0.2316736622836535468765376j)
+
**References**

1. [DLMF]_ section 25.14
@@ -1117,13 +1132,11 @@
"""
if z == 0:
return a ** (-s)
- """
# Faster, but these cases are useful for testing right now
if z == 1:
return ctx.zeta(s, a)
if a == 1:
- return z * ctx.polylog(s, z)
- """
+ return ctx.polylog(s, z) / z
if ctx.re(a) < 1:
if ctx.isnpint(a):
raise ValueError("Lerch transcendent complex infinity")