Opened 7 years ago

Last modified 7 years ago

#16197 closed enhancement

provide function expansions of power series (from Pari) — at Initial Version

Reported by: rws Owned by:
Priority: major Milestone: sage-duplicate/invalid/wontfix
Component: calculus Keywords: function, series expansion
Cc: Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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Not the same as SR.taylor().

sage: R.<x> = PowerSeriesRing(ZZ)
sage: sqrt(1-4*x^2)
1 - 2*x^2 - 2*x^4 - 4*x^6 - 10*x^8 - 28*x^10 - 84*x^12 - 264*x^14 - 858*x^16 - 2860*x^18 + O(x^20)
sage: sin(1+4*x^2)
TypeError: cannot coerce arguments: no canonical coercion from Power Series Ring in x over Integer Ring to Symbolic Ring
sage: var('X')
sage: ex=sin(1+4*X^2)
sage: ex.series()
TypeError: series() takes exactly 2 positional arguments (0 given)

What is missing and can be had from Pari:

  • acos, acosh, agm, asin, asinh, atan, atanh, cos, cosh, cotanh, dilog, gamma, intformal, lngamma, psi, sin, sinh, tan, tanh

For example:

? atan(4*x^2+1)
%1 = 0.78539816339744830961566084581987572105 + 2*x^2 - 4*x^4 + 16/3*x^6 - 128/5*x^10 + 256/3*x^12 - 1024/7*x^14 + O(x^16)

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