implement symbolic Stieltjes constants

[rwst]

Probably just another symbolic function would suffice. This would be needed for zeta expansion and special values. The Sage side would be a new GinacFunction and numeric evaluation.

• https://en.wikipedia.org/wiki/Stieltjes_constants
• http://docs.sympy.org/dev/modules/mpmath/functions/zeta.html#stieltjes
• Section 4.2 of http://arxiv.org/abs/1309.2877

Depends on pynac/pynac#120
See also #18141.

Depends on #19948

CC: @behackl

Component: symbolics

Author: Ralf Stephan

Branch/Commit: 0e1162b

Reviewer: Benjamin Hackl

Issue created by migration from https://trac.sagemath.org/ticket/19834

[rwst]

Description changed:

--- 
+++ 
@@ -4,4 +4,8 @@
 
 This would be needed for zeta expansion and special values.
 
-See also #18141
+Depends on https://github.com/pynac/pynac/issues/120
+
+The Sage side would be a new `GinacFunction`. 
+
+See also #18141.

[rwst]

Description changed:

--- 
+++ 
@@ -1,11 +1,5 @@
-Probably just another symbolic function would suffice.
-
-https://en.wikipedia.org/wiki/Stieltjes_constants
-
-This would be needed for zeta expansion and special values.
+Probably just another symbolic function would suffice. This would be needed for zeta expansion and special values. The Sage side would be a new `GinacFunction` and numeric evaluation. Section 4.2 of http://arxiv.org/abs/1309.2877 would be the starting point of the latter.
 
 Depends on https://github.com/pynac/pynac/issues/120
-
-The Sage side would be a new `GinacFunction`. 
-
 See also #18141.
+https://en.wikipedia.org/wiki/Stieltjes_constants

[rwst]

Description changed:

--- 
+++ 
@@ -1,5 +1,8 @@
-Probably just another symbolic function would suffice. This would be needed for zeta expansion and special values. The Sage side would be a new `GinacFunction` and numeric evaluation. Section 4.2 of http://arxiv.org/abs/1309.2877 would be the starting point of the latter.
+Probably just another symbolic function would suffice. This would be needed for zeta expansion and special values. The Sage side would be a new `GinacFunction` and numeric evaluation.
+
+* https://en.wikipedia.org/wiki/Stieltjes_constants
+* http://docs.sympy.org/dev/modules/mpmath/functions/zeta.html#stieltjes
+* Section 4.2 of http://arxiv.org/abs/1309.2877
 
 Depends on https://github.com/pynac/pynac/issues/120
 See also #18141.
-https://en.wikipedia.org/wiki/Stieltjes_constants

[behackl]

comment:5

For the sake of representation: should there be two separate functions, say stieltjes(n) and generalized_stieltjes(n, a) represented as \gamma_n and \gamma_n(a), respectively?

Of course, like stieltjes(0) should return euler_gamma, generalized_stieltjes(n, 1) should return stieltjes(n) -- but I think this can be done easily, either still in pynac, or after registering the function in sage.

[behackl]

comment:6

... or just stieltjes(n, a=1) with adaptive representation. That's probably more elegant. ;-)

[rwst]

Branch: u/rws/implement_symbolic_stieltjes_constants

[rwst]

Author: Ralf Stephan

[rwst]

comment:8

This is what Sage needs to use the current pynac git master implementation of Stieltjes constants (not generalized).

---

New commits:

bdac71f

19834: implement symbolic Stieltjes constants

[rwst]

Commit: bdac71f

[rwst]

Dependencies: pynac-0.6.1