| abs(x) | int or real | |x|, absolute value of x; same type |
| abs(x) | complex | length of x, √( Re(x)2 + Im(x)2 ) |
| acos(x) | any | cos-1 x (inverse cosine) |
| acosh(x) | any | cosh-1 x (inverse hyperbolic cosine) |
| airy(x) | real | Airy function Ai(x) for real 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) |
| 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) |
| besj0(x) | real | J0 Bessel function of x in radians |
| besj1(x) | real | J1 Bessel function of x in radians |
| besjn(n,x) | int,real | Jn Bessel function of x in radians |
| besy0(x) | real | Y0 Bessel function of x in radians |
| besy1(x) | real | Y1 Bessel function of x in radians |
| besyn(n,x) | int,real | Yn 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 |
| cbrt(x) | real | cube root of x, domain and range both real |
| ceil(x) | any | ⌈x⌉, smallest integer not less than x (real part) |
| conj(x) | complex | complex conjugate of x |
| cos(x) | radians | cos x, cosine of x |
| cosh(x) | any | cosh x, hyperbolic cosine of x 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) | Π(n,k) complete elliptic integral of the third kind |
| erf(x) | any | erf(Re(x)), error function of real(x) |
| erfc(x) | any | erfc(Re(x)), 1.0 - error function of real(x) |
| exp(x) | any | ex, exponential function of x |
| expint(n,x) | any | En(x), exponential integral function of x |
| floor(x) | any | ⌊x⌋, largest integer not greater than x (real part) |
| gamma(x) | any | Γ(Re(x)), gamma function of real(x) |
| ibeta(p,q,x) | any | ibeta(Re(p,q,x)), ibeta function of real(p,q,x) |
| inverf(x) | any | inverse error function real(x) |
| igamma(a,z) | complex | igamma(a>0,z), igamma function of complex a>0,z |
| imag(x) | complex | Im(x), imaginary part of x as a real number |
| int(x) | real | integer part of x, truncated toward zero |
| invibeta(a,b,p) | 0<p<1 | inverse incomplete beta function |
| invigamma(a,p) | 0<p<1 | inverse incomplete gamma function |
| invnorm(x) | any | inverse normal distribution function real(x) |
| LambertW(z,k) | complex, int | kth branch of complex Lambert W function |
| lambertw(x) | real | principal branch (k=0) of Lambert W function |
| lgamma(x) | real | lgamma(Re(x)), lgamma function of real(x) |
| lnGamma(x) | complex | lnGamma(x) valid over entire complex plane |
| log(x) | any | ln x, natural logarithm (base e) of x |
| log10(x) | any | log10 x, logarithm (base 10) of x |
| norm(x) | any | norm(x), normal distribution function of real(x) |
| rand(x) | int | pseudo random number in the interval (0:1) |
| real(x) | any | Re(x), real part of x |
| sgn(x) | any | 1 if x > 0, -1 if x < 0, 0 if x = 0. ℑ(x) ignored |
| Sign(x) | complex | 0 if x = 0, otherwise x/|x| |
| sin(x) | any | sin x, sine of x |
| sinh(x) | any | sinh x, hyperbolic sine of x in radians |
| sqrt(x) | any | √x, square root of x |
| SynchrotronF(x) | real | Synchtrotron function F |
| tan(x) | any | tan x, tangent of x |
| tanh(x) | any | tanh x, hyperbolic tangent of x in radians |
| uigamma(a,x) | real | uigamma(a,x), upper incomplete gamma function a>0,x |
| voigt(x,y) | real | convolution of Gaussian and Lorentzian |
| zeta(s) | any | Riemann zeta function |