arb_lambertw

acb_lambertw

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

math

An R interface to 'FLINT' <https://flintlib.org/>, a C library for
number theory. 'FLINT' extends GNU 'MPFR' <https://www.mpfr.org/>
and GNU 'MP' <https://gmplib.org/> with support for operations on
standard rings (the integers, the integers modulo n, finite
fields, the rational, p-adic, real, and complex numbers) as well
as matrices and polynomials over rings. 'FLINT' implements
midpoint-radius interval arithmetic, also known as ball
arithmetic, in the real and complex numbers, enabling computation
in arbitrary precision with rigorous propagation of rounding and
other errors; see Johansson (2017) <doi:10.1109/TC.2017.2690633>.
Finally, 'FLINT' provides ball arithmetic implementations of many
special mathematical functions, with high coverage of reference
works such as the NIST Digital Library of Mathematical Functions
<https://dlmf.nist.gov/>. The R interface defines S4 classes,
generic functions, and methods for representation and basic
operations as well as plain R functions mirroring and vectorizing
entry points in the C library.

Mikael Jagan

flint

Fast Library for Number Theory

Martin Maechler

arb_lambertw function

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

Arguments

Lambert W function — arb_lambertw

<dl>

 <dt>x, z</dt>
<dd>numeric, complex, <code>arb</code>, or
 <code>acb</code> vectors.</dd>

 <dt>k</dt>
<dd>an integer or <code>fmpz</code> vector listing indices
 of branches of the function. <code>0</code> indicates the principal
 branch.</dd>

 <dt>flags</dt>
<dd>for <code>arb_lambertw</code>: 
 an integer vector indicating which of the index 0 and index -1
 branches is computed (<code>0</code> means index 0, <code>1</code> means index
 -1). 
 
 for <code>acb_lambertw</code>: 
 an integer vector indicating how branch cuts are defined.
 Nonzero values are nonstandard; see the first reference.</dd>

 <dt>prec</dt>
<dd>a numeric or <code>slong</code> vector indicating the
 desired precision as a number of bits.</dd>

</dl>

arb_lambertw: Lambert W function

Description

Usage

Value

Arguments

References

See Also

Examples