oldk1331 wrote:
>
> (1) -> limit(atan(sqrt(1-J*z)/sqrt(J-1)),z=1,"left")
>
> +-------+
> \|- J + 1
> (1) log(- ----------)
> +-----+
> 2\|J - 1
> Type: Union(OrderedCompletion(Expression(Integer)),...)
> (2) -> limit(asin(sqrt(1-J*z)/sqrt(J-1)),z=1,"left")
>
> +-------+
> \|- J + 1
> (2) asin(----------)
> +-----+
> \|J - 1
> Type: Union(OrderedCompletion(Expression(Integer)),...)
>
>
> This bug originates from mapleok.input:
> in1638a:=integrate(-z/(z-1)/(1-I*z)^(1/2), z= 0..1,"noPole")
>
> The limit is wrong for atan, if you change atan to other functions,
> then no errors. The argument for atan is not special.
> I tried to debug this, but nothing special happens.
> I trace directly to "limitPlus", the series expansion does
> not fail, and the reuslt is "coefficient(upxs, 0)".
I as wrote, there is a lot of GIGO in 'mapleok.input'. 'limit'
assumes real functions, but for z close to 1 values of
'sqrt(1-J*z)/sqrt(J-1)' are complex (or undefined). Namely,
for J = 1 we have division by 0, for J < 1 denomiator is
square root of negative number and for J > 1 limit of
1-J*z is negative. Depending on J and choice of branch
cut the limit of argument is +-%i, that is singularities
of 'atan'. The true limit is complex infinity, going
along imaginary axis. 'asin' is regular at +-%i so the result.
--
Waldek Hebisch
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