simplify_hypergeometric bug

[rwst]

The result of expansion of a 2F1 expression using simplify_hypergeometric differs from computing the numeric directly:

sage: hypergeometric((1/5, 4/5), (6/5,), 1/10*sqrt(5)*(sqrt(5) - 1))
hypergeometric((1/5, 4/5), (6/5,), 1/10*sqrt(5)*(sqrt(5) - 1))
sage: _.n()
1.04296605906833
sage: hypergeometric((1/5, 4/5), (6/5,), 1/10*sqrt(5)*(sqrt(5) - 1))
hypergeometric((1/5, 4/5), (6/5,), 1/10*sqrt(5)*(sqrt(5) - 1))
sage: _.simplify_hypergeometric()
0

Inside maxima:

maxima: hgfred([1/5, 4/5], [6/5], 1/10*sqrt(5)*(sqrt(5) - 1));
((1-(sqrt(5)-1)/(2*sqrt(5)))^(1/10)*assoc_legendre_p(-4/5,-1/5,1-(sqrt(5)-1)/sqrt(5))*gamma(1/5))/(5*((sqrt(5)-1)/(2*sqrt(5)))^(1/10))

CC: @slel

Component: calculus

Reviewer: Dima Pasechnik

Issue created by migration from https://trac.sagemath.org/ticket/22467

[rwst]

comment:1

User error. Assumptions given earlier interferred with simplify_hypergemetric.

[rwst]

comment:3

Hijacking ticket to prevent waste. Quite a similar error, this time for real.

[rwst]

Description changed:

--- 
+++ 
@@ -1,25 +1,13 @@
 The result of expansion of a `2F1` expression using `simplify_hypergeometric` differs when substituting `x` with a numeric versus computing the numeric directly:
 
 ```
-sage: hypergeometric((-1/3,4/3),(7/3,),x)
-hypergeometric((-1/3, 4/3), (7/3,), x)
+sage: hypergeometric((1/5, 4/5), (6/5,), 1/10*sqrt(5)*(sqrt(5) - 1))
+hypergeometric((1/5, 4/5), (6/5,), 1/10*sqrt(5)*(sqrt(5) - 1))
+sage: _.n()
+1.04296605906833
+sage: hypergeometric((1/5, 4/5), (6/5,), 1/10*sqrt(5)*(sqrt(5) - 1))
+hypergeometric((1/5, 4/5), (6/5,), 1/10*sqrt(5)*(sqrt(5) - 1))
 sage: _.simplify_hypergeometric()
-4/9*(-x + 1)^(2/3)*gen_legendre_P(1/3, -4/3, -2*x + 1)*gamma(1/3)/(-x)^(2/3)      # not verified
-sage: _.subs(x==-5/11)
-176/45*(5/11)^(1/3)*(2/11)^(2/3)*gen_legendre_P(1/3, -4/3, 21/11)*gamma(1/3)
-sage: _.n(200)
--0.53941834251374840921300901563397867197519834837178347048562 + 0.93429997576840318754064074204329937894765008653252481028466*I
-sage: hypergeometric((-1/3,4/3),(7/3,),-5/11)
-hypergeometric((-1/3, 4/3), (7/3,), -5/11)
-sage: _.n(200)     # verified by Alpha
-1.0788366850274968184260180312679573439503966967435669409712
-sage: (5/11)^(1/3)*(2/11)^(2/3)
-(5/11)^(1/3)*(2/11)^(2/3)
-sage: _.n(200)
-0.24676523787226423377437176997086265498228252449900881429858
-sage: gen_legendre_P(1/3, -4/3, 21/11)
-gen_legendre_P(1/3, -4/3, 21/11)
-sage: _.n(200)     # verified by Alpha
--0.20863099380558942774105138711985994226338270038962969500434 + 0.36135948130486860453162137841966370046727111778651381582091*I
+0
 ```
-Is the expansion wrong?
+