arb_lambertw: Lambert W function

In flint: Fast Library for Number Theory

Lambert W function

Description

Computes any branch W_{k} of the multiple-valued Lambert W function. W(z) is the set of solutions w of the equation w e^{w} = z.

Usage

arb_lambertw(x,         flags = 0L, prec = flintPrec())
acb_lambertw(z, k = 0L, flags = 0L, prec = flintPrec())

Arguments

x, z	numeric, complex, arb, or acb vectors.
k	an integer or fmpz vector listing indices of branches of the function. 0 indicates the principal branch.
flags	for arb_lambertw: an integer vector indicating which of the index 0 and index -1 branches is computed (0 means index 0, 1 means index -1). for acb_lambertw: an integer vector indicating how branch cuts are defined. Nonzero values are nonstandard; see the first reference.
prec	a numeric or slong vector indicating the desired precision as a number of bits.

Value

An arb or acb vector storing function values with error bounds. Its length is the maximum of the lengths of the arguments or zero (zero if any argument has length zero). The arguments are recycled as necessary.

References

The FLINT documentation of the underlying C functions: https://flintlib.org/doc/arb.html, https://flintlib.org/doc/acb.html

NIST Digital Library of Mathematical Functions: https://dlmf.nist.gov/4.13

See Also

Classes arb and acb.

Examples

## TODO

flint documentation built on June 8, 2025, 1:27 p.m.