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The principal branch of Lambert’s W function W(z) (DLMF 4.13), the solution of $$ z = W(z)e^{W(z)} $$
The k-th branch of Lambert’s W function W(z) (DLMF 4.13), the solution of \(z=W(z)e^{W(z)}\).
The principal branch, denoted 
\(W_p(z)\) in DLMF, is lambert_w(z) = generalized_lambert_w(0,z).
The other branch with real values, denoted 
\(W_m(z)\) in DLMF, is generalized_lambert_w(-1,z).
The Bateman k function
$$ k_v(x) = \frac{2}{\pi} \int_0^{\frac{\pi}{2}} \cos(x \tan\theta-v\theta)d\theta $$It is a special case of the confluent hypergeometric function. Maxima can
calculate the Laplace transform of kbateman using laplace
or specint, but has no other knowledge of this function.
The Plasma Dispersion Function $$ {\rm nzeta}(z) = i\sqrt{\pi}e^{-z^2}(1-{\rm erf}(-iz)) $$
Returns realpart(nzeta(z)).
Returns imagpart(nzeta(z)).
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