arb_lambertw function

Lambert W function

Computes any branch $W_k$ of the multiple-valued Lambert $W$ function. $W(z)$ is the set of solutions $w$ of the equation $w * exp(w) = z$.

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.

Returns

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.

See Also

Classes arb and acb.

References

The FLINT documentation of the underlying

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

Examples

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