Result depends on the sign of I

[Paul Royik]

I see this error when try to calculate limit of (-1)^x /sqrt(x) as x approaches infinity.

Can somebody explain me what is the problem here?

[Kalevi Suominen]

On Monday, September 7, 2015 at 9:37:58 AM UTC+3, Paul Royik wrote:

I see this error when try to calculate limit of (-1)^x /sqrt(x) as x approaches infinity.

Can somebody explain me what is the problem here?

``(-1)^x`` is equal to ``exp(pi*I*x)``. As the function has no serial expansion at infinity, SymPy attempts to use Gruntz' algorithm. It is intended tor real functions, and SymPy assumes that everything is real. It knows that ``pi`` is real and positive and the same is assumed of ``x``. That leaves just one problem: what is the sign of I.

Actually, there is currently no algorithm in SymPy capable of computing the limit (which is 0 as ``x`` tends to ``oo`` on the real line),

[Paul Royik]

Thank you.

[Aaron Meurer]

You can compute the limit by expanding the real and imaginary parts:

In [19]: x = Symbol('x', real=True, positive=True)

In [20]: expand(exp(pi*I*x)/sqrt(x), complex=True)
Out[20]:
ⅈ⋅sin(π⋅x) cos(π⋅x)
────────── + ────────
√x √x

In [21]: limit(expand(exp(pi*I*x)/sqrt(x), complex=True), x, oo)
Out[21]: 0

Aaron Meurer

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