calculate asymptotic expansions to some asymptotic expansions exponents directly

[dkrenn]

Make

sage: (1+1/n^2)^n

and related be calculated directly.

Depends on #20043

CC: @behackl @cheuberg

Component: asymptotic expansions

Author: Daniel Krenn

Branch/Commit: 29bffe0

Reviewer: Clemens Heuberger

Issue created by migration from https://trac.sagemath.org/ticket/20044

[dkrenn]

Branch: u/dkrenn/asy/pow-var

[sagetrac-git]

Commit: c6ca928

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

98591d6	Trac #20044: NoConvergenceError
69c090c	Trac #20044: extend `__pow_number__` and test for convergence
7ed3541	Trac #20044: add shortcuts for exponents 0 and 1 in __pow__
3f7a661	Trac #20044: use new extension in __pow__
c6ca928	Merge branch 'u/dkrenn/asy/one-times-zero' of git://trac.sagemath.org/sage into t/20044/asy/pow-var

[dkrenn]

Dependencies: #20043

[cheuberg]

Changed branch from u/dkrenn/asy/pow-var to u/cheuberg/asy/pow-var

[cheuberg]

comment:5

Proving mathematical correctness is not completely trivial: if one rewrites it as exp( exponent*log(1+x)), this is no problem. And expanding these exponential function and logarithms leads to some monomials in x and exponent. The error is O((exponent + exponent<sup>K)*x</sup>K) if K is the number of exact summands in the binomial series. Both of these error terms actually occur in the binomial expansion, so everything is fine.

Added a minor commit (one comma removed); the rest is fine.

---

New commits:

29bffe0

Trac #20044: punctuation

[cheuberg]

Reviewer: Clemens Heuberger

[cheuberg]

Changed commit from c6ca928 to 29bffe0

[vbraun]

Changed branch from u/cheuberg/asy/pow-var to 29bffe0