Complex functions at z = 0

Complex valued special functions about a point.

boring_math.special_functions.complex0.exp0(z: complex, /, n: int = 22) → complex

Partially factored Taylor expansion of exp about z = 0.

Note

Best if |z| <= 1.

Parameters:

• z – independent variable

• n – terms in expansion, must have n >= 20

Returns:

Taylor series expansion of eᶻ centered at z = 0

boring_math.special_functions.complex0.sin0(z: complex, /, n: int = 22) → complex

Partially factored Taylor expansion of sine about z = 0.

Note

Best if |z| <= 2π.

Parameters:

• z – independent variable

• n – terms in expansion, must have 2 <= n <= 20

Returns:

Taylor series expansion of sine(x) centered at z = 0

boring_math.special_functions.complex0.cos0(z: complex, /, n: int = 22) → complex

Partially factored Taylor expansion of cosine about z = 0.

Note

Best if |z| <= 2π.

Parameters:

• z – independent variable

• n – terms in expansion, must have 2 <= n <= 20

Returns:

Taylor series expansion of cosine(z) centered at z = 0

boring_math.special_functions.complex0.tan0(z: complex, /, n: int = 22) → complex

Tangent centered about z = 0.

Note

Best if |z| <= π.

Parameters:

• z – independent variable

• n – terms in expansion, must have 2 <= n <= 20

Returns:

sin0(z)/cos0(z)