mathxlab.num.series

Numerical series and Taylor approximation helpers.

Stability

Status: Experimental.

This project treats the documented names as the public surface, but details may still evolve. If you need strict API guarantees, add __all__ = [...] to each module and version releases accordingly.

Design notes

  • Keep helpers small, explicit, and reproducible.

Examples

Taylor polynomial approximation of sin(x)

import numpy as np
from mathxlab.num.series import taylor_sin
print(taylor_sin(np.array([0.0, 1.0]), x0=0.0, degree=7))

Public API

Name

Kind

Summary

taylor_sin

function

Compute the Taylor polynomial approximation of sin(x) around x0.

Reference

Functions

mathxlab.num.series.taylor_sin(x, x0, degree)[source]

Compute the Taylor polynomial approximation of sin(x) around x0.

Uses a direct series expansion:

sin(x) = sum_k (-1)^k (x-x0)^(2k+1) / (2k+1)! (about x0 for shifted variable)

Note

This is intentionally simple for experiment purposes (not optimized).

Parameters:

  • x – Input array.

  • x0 – Expansion point.

  • degree – Polynomial degree (non-negative).

Returns:

Array of Taylor approximation values at x.

Examples

>>> import numpy as np
>>> from mathxlab.num.series import taylor_sin
>>> float(taylor_sin(np.array([0.1]), 0.0, 5)[0])