Mathematical Functions

Table 4.2. 

Name Description
abs(x) absolute value of x
acos(x) inverse cosinus
acosh(x) inverse hyperbolic cosinus
asin(x) inverse sinus
asinh(x) inverse hyperbolic sinus
atan(x) inverse tangent
atanh(x) inverse hyperbolic tangent
avg(x1,x2,x3,...) average value, this command accept a list of arguments separated by commas
bessel_j0(x) Regular cylindrical Bessel function of zeroth order, J0(x).
bessel_j1(x) Regular cylindrical Bessel function of first order, J1(x).
bessel_jn(x,n) Regular cylindrical Bessel function of nth order, Jn(x).
bessel_jn_zero(n, s) sth zero of regular cylindrical Bessel function of nth order, Jn(bessel_jn_zero(n,s))=0
bessel_y0(x) Irregular cylindrical Bessel function of zeroth order, Y0(x) for x>0.
bessel_y1(x) Irregular cylindrical Bessel function of first order, Y1(x) for x>0.
bessel_yn(x,n) Irregular cylindrical Bessel function of nth order, Yn(x) for x>0.
beta (a,b) Computes the Beta Function, B(a,b) = Gamma(a)*Gamma(b)/Gamma(a+b) for a > 0 and b > 0.
ceil(x) ceiling; smallest integer greater or equal to x
cos(x) cosinus of x
cosh(x) hyperbolic cosinus of x
erf(x) error function of x
erfc(x) Complementary error function erfc(x) = 1 - erf(x).
erfz(x) The Gaussian probability density function Z(x).
erfq(x) The upper tail of the Gaussian probability function Q(x).
exp(x) Exponential function: e raised to the power of x.
floor(x) floor; largest integer less than or equal to x
gamma(x) Computes the Gamma function, subject to x not being a negative integer
gammaln(x) Computes the logarithm of the Gamma function, subject to x not a being negative integer. For x<0, log(|Gamma(x)|) is returned.
hazard(x) Computes the hazard function for the normal distribution h(x) = erfz(x)/erfq(x).
ln(x) natural logarythm of x
log(x) decimal logarythm of x
log2(x) base 2 logarythm of x
w0(x) Principal branch of Lambert's W function, W0(x). W0 is defined as a solution to the equation W0(x)*exp(W0(x))=x. For x<0, there are tow real-valued branches; this function computes the one where W>-1 for x<0 (compare w1(x)).
w1(x) Secondary branch of Lambert's W function, W-1(x). W-1 is defined as a solution to the equation W-1(x)*exp(W-1(x))=x. For x<0, there are tow real-valued branches; this function computes the one where W<-1 for x<0 (compare w0(x)).
min(x1,x2,x3,...) Minimum of the list of arguments
max(x1,x2,x3,...) Maximum of the list of arguments
mod(x,y) x modulo y; remainder of integer division x/y
pow(x,y) x to the power of y, x^y
rint(x) Round to nearest integer.
sign(x) Sign function: -1 if x<0; 1 if x>0.
sin(x) sinus of x
sinh(x) hyperblic sinus of x
sqrt(x) square root of x
tan(x) tangent of x
tanh(x) hyperbolic tangent of x