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\begin{longtable}{|ccl|} \hline
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Function & Arguments & Returns \\\hline
\endhead \hline \endfoot

abs(x) & any  &  absolute value of $x$, $|x|$; same type \\
abs(x) & complex &  length of $x$, $\sqrt{{\mbox{real}(x)^{2} +
\mbox{imag}(x)^{2}}}$\  \\

acos(x) & any  & $\cos^{-1} x$\  (inverse cosine) \\

acosh(x) & any  & $\cosh^{-1} x$\  (inverse hyperbolic cosine) in radians \\

airy(x) & any  & Airy function Ai(x) \\

arg(x) & complex & the phase of $x$\  \\

asin(x) & any  & $\sin^{-1} x$\  (inverse sin) \\

asinh(x) & any  & $\sinh^{-1} x$\  (inverse hyperbolic sin) in radians \\

atan(x) & any  & $\tan^{-1} x$\  (inverse tangent) \\

atan2(y,x) & int or real & $\tan^{-1} (y/x)$\  (inverse tangent) \\

atanh(x) & any  & $\tanh^{-1} x$\  (inverse hyperbolic tangent) in radians \\

EllipticK(k) & real k $\in$\  (-1:1) & $K(k)$\  complete elliptic integral of the first kind \\

EllipticE(k) & real k $\in$\  [-1:1] & $E(k)$\  complete elliptic integral of the second kind \\

EllipticPi(n,k) & real n$<$1, real k $\in$\  (-1:1) & $\Pi(n,k)$\  complete elliptic integral of the third kind \\

 besj0(x) & int or real &  $J_{0}$\  Bessel function of $x$\  in radians \\

 besj1(x) & int or real & $J_{1}$\  Bessel function of $x$\  in radians \\

 besjn(n,x) & int, real & $J_{n}$\  Bessel function of $x$\  in radians \\

 besy0(x) & int or real & $Y_{0}$\  Bessel function of $x$\  in radians \\

 besy1(x) & int or real & $Y_{1}$\  Bessel function of $x$\  in radians \\

 besyn(n,x) & int, real & $Y_{n}$\  Bessel function of $x$\  in radians \\

 besi0(x) &real & Modified Bessel function of order 0, $x$\  in radians \\

 besi1(x) &real & Modified Bessel function of order 1, $x$\  in radians \\

 besin(n,x) &int, real & Modified Bessel function of order n, $x$\  in radians \\

ceil(x) & any & $\lceil x \rceil$, smallest integer not less than $x$
(real part) \\

cos(x) & any & $\cos x$, cosine of $x$\  \\

cosh(x) & any & $\cosh x$, hyperbolic cosine of $x$\  in radians \\

erf(x) & any & $\mbox{erf}(\mbox{real}(x))$,  error function of real($x$) \\

erfc(x) & any & $\mbox{erfc}(\mbox{real}(x))$,  1.0 - error function of real($x$) \\

exp(x) & any & $e^{x}$,  exponential function of $x$\  \\

expint(n,x) & int $n\ge0$, real $x\ge0$\  & $E_n(x)=\int_1^\infty t^{-n} e^{-xt}\,dt$,  exponential integral of $x$\  \\

floor(x) & any & $\lfloor x \rfloor$,  largest integer not greater
than $x$\  (real part) \\

gamma(x) & any & $\mbox{gamma}(\mbox{real}(x))$,  gamma function of real($x$) \\

ibeta(p,q,x) & any & $\mbox{ibeta}(\mbox{real}(p,q,x))$,  ibeta function of real($p$,$q$,$x$) \\

inverf(x) & any &  inverse error function of real($x$)  \\

igamma(a,x) & any & $\mbox{igamma}(\mbox{real}(a,x))$,  igamma function of real($a$,$x$) \\

imag(x) & complex &  imaginary part of $x$\  as a real number \\

invnorm(x) & any &  inverse normal distribution function of real($x$)  \\

int(x) & real &  integer part of $x$, truncated toward zero \\

lambertw(x) & real & Lambert W function \\

lgamma(x) & any & $\mbox{lgamma}(\mbox{real}(x))$,  lgamma function of real($x$) \\

log(x) & any & $\log_{e} x$,  natural logarithm (base $e$) of $x$\  \\

log10(x) & any & $\log_{10} x$,  logarithm (base $10$) of $x$\  \\

norm(x) & any & normal distribution (Gaussian) function of real($x$) \\

rand(x) & int & pseudo random number in the open interval (0:1) \\

real(x) & any &  real part of $x$\  \\

sgn(x) & any & 1 if $x>0$, -1 if $x<0$, 0 if $x=0$. imag($x$) ignored \\

sin(x) & any & $\sin x$, sine of $x$\  \\

sinh(x) & any & $\sinh x$, hyperbolic sine of $x$\  in radians \\

sqrt(x) & any & $\sqrt{x}$,  square root of $x$\  \\

tan(x) & any & $\tan x$,  tangent of $x$\  \\

tanh(x) & any & $\tanh x$, hyperbolic tangent of $x$\  in radians\\

voigt(x,y) & real & Voigt/Faddeeva function $\frac{y}{\pi} \int{\frac{exp(-t^2)}{(x-t)^2+y^2}}dt$\  \\
           &       & Note: voigt$(x,y)$\  = $real($faddeeva$(x+iy))$\  \\
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cerf(z) & complex &  complex error function \\

cdawson(z)&complex&complex extension of Dawson's integral $D(z)={\frac{\sqrt{\pi}}{2}e^{-z^2} erfi(z)} $\  \\

faddeeva(z)&complex&rescaled complex error function $w(z) = e^{-z^2}~ erfc(-iz) $\  \\

erfi(x)&real&imaginary error function $erf(x) = -i * erf(ix)$\  \\

VP(x,$\sigma$,$\gamma$)&real& Voigt profile $ VP(x,\sigma,\gamma) = {\int^{\infty}_{-\infty}{G(x^\prime;\sigma) L(x-x^\prime;\gamma) dx^\prime }} $\  \\
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