Status: Valid
Owner: ----
Labels: Type-Defect Priority-Medium Series
New issue 3918 by someb...@bluewin.ch: Another gamma limit
http://code.google.com/p/sympy/issues/detail?id=3918
Sympy can not do the following limit:
In [92]: G = gamma(n - x + 1)*gamma(n + x + 1)/gamma(n + 1)**2
In [93]: limit(G, n, oo)
Out[93]: 0
In [96]: gruntz(G, n, oo)
Out[96]: 0
There is reason to believe the correct value is 1.
Axiom / Fricas fails:
(1) -> G := Gamma(1+n-x)*Gamma(1+n+x)/Gamma(1+n)^2
Gamma(- x + n + 1)Gamma(x + n + 1)
(1) ----------------------------------
2
Gamma(n + 1)
Type:
Expression(Integer)
(2) -> limit(G, n=%plusInfinity)
(2) "failed"
Type:
Union("failed",...)
(3) -> mrv_limit(G, n=%plusInfinity)
(3) "failed"
Type:
Union("failed",...)
Maxima fails:
(%i24) G;
gamma(- x + n + 1) gamma(x + n + 1)
(%o24) -----------------------------------
2
gamma (n + 1)
(%i25) limit(G, n, inf);
(%o25) inf
If we assume an arbitrary value for x, then sympy can do it:
In [98]: G.subs(x, 23)
Out[98]: gamma(n - 22)*gamma(n + 24)/gamma(n + 1)**2
In [99]: limit(_, n, oo)
Out[99]: 1
Axiom / Fricas can not:
(9) -> subst(G, x=23)
Gamma(n - 22)Gamma(n + 24)
(9) --------------------------
2
Gamma(n + 1)
Type:
Expression(Integer)
(10) -> limit(%, n=%plusInfinity)
(10) "failed"
Type:
Union("failed",...)
(11) -> subst(G, x=23)
Gamma(n - 22)Gamma(n + 24)
(11) --------------------------
2
Gamma(n + 1)
Type:
Expression(Integer)
(12) -> mrv_limit(%, n=%plusInfinity)
(12) "failed"
Type:
Union("failed",...)
And maxima can:
(%i2) G : gamma(1+n-23)*gamma(1+n+23)/gamma(1+n)^2;
gamma(n - 22) gamma(n + 24)
(%o2) ---------------------------
2
gamma (n + 1)
(%i3) limit(%, n, inf);
(%o3) 1
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