| abs(x) |
any |
\(|x|\), absolute value of \( x \); same type |
| abs(x) |
complex |
\(\sqrt{\text{real}(x)^2 + \text{imag}(x)^2}\) |
| acos(x) |
any |
\(\cos^{-1}(x)\) (inverse cosine) |
| acosh(x) |
any |
\(\cosh^{-1}(x)\) (inverse hyperbolic cosine) |
| airy(x) |
any |
Airy function \( \text{Ai}(x) \) |
| arg(x) |
complex |
the phase of \( x \) |
| asin(x) |
any |
\(\sin^{-1}(x)\) (inverse sine) |
| asinh(x) |
any |
\(\sinh^{-1}(x)\) (inverse hyperbolic sine) |
| 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) |
| 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 \( x \) |
| erf(x) |
any |
\(\text{erf(real}(x))\), error function of \(\text{real}(x)\) |
| erfc(x) |
any |
\(\text{erfc(real}(x))\), \(1.0 - \) error function of \(\text{real}(x)\) |
| exp(x) |
any |
\(e^x\), exponential function of \( x \) |
| expint(n, x) |
int \( n \geq 0 \), real \( x \geq 0 \) |
\(E_n(x) = \int_1^{\infty} t^{-n} e^{-xt} \, dt\), exponential integral of \( x \) |
| floor(x) |
any |
\(\lfloor x \rfloor\), largest integer not greater than \( x \) (real part) |
| gamma(x) |
any |
\(\text{gamma(real}(x))\), gamma function of \(\text{real}(x)\) |
| ibeta(p, q, x) |
any |
\(\text{ibeta}(p, q, x)\), beta function of \( (p, q, x) \) |
| inverf(x) |
any |
inverse error function of \(\text{real}(x)\) |
| igamma(a, x) |
any |
\(\text{igamma(real}(a, x))\), igamma function of \(\text{real}(a, x)\) |
| imag(x) |
complex |
imaginary part of \( x \) as a real number |
| invnorm(x) |
any |
inverse normal distribution function of \(\text{real}(x)\) |
| int(x) |
real |
integer part of \( x \), truncated toward zero |
| lambertw(x) |
real |
Lambert \( W \) function |
| lgamma(x) |
any |
\(\text{lgamma(real}(x))\), lgamma function of \(\text{real}(x)\) |
| 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 \(\text{real}(x)\) |
| 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 \( x = 0 \). \(\text{imag}(x)\) 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 |