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Xnumbers Tutorial
273
sqr(x)
R C M square root
sqr(2) =1.4142135623731, also 2^(1/2)
tan(x)
R C M tangent
argument (in radians) x≠ k*π/2 with k =
±
1,
±
2…
tanh(x)
R C M hyperbolic tangent
xor(a,b)
R
logic exclusive-or
returns 1 (true) only if a ≠ b
BesselI(x,n)
R
Bessel's function of 1st kind, nth
order, mod.
x >0 , n = 0,1, 2, 3…
BesselJ(x,n)
R
Bessel's function of 1st kind, nth
order
x ≥0 , n = 0, 1, 2, 3…
BesselK(x,n)
R
Bessel's function of 2nd kind, nth
order, mod.
x >0 , n = 0,1, 2, 3…
BesselY(x,n)
R
Bessel's function of 2nd kind, nth
order
x ≥0 , n = 0,1, 2, 3…
J0(x)
R
Bessel's function of 1st kind
x ≥0
Y0(x)
R
Bessel's function of 2nd kind
x ≥0
I0(x)
R
Bessel's function of 1st kind, modified x >0
K0(x)
R
Bessel's function of 2nd kind,
modified
x >0
Si(x)
R
Sine integral
∀ x
Ci(x)
R
Cosine integral
x >0
zeta(x)
R
Riemman's zeta function
argument x<-1 or x>1
AiryA(x)
R
Airy function Ai(x)
∀x, example cbr(2) = 1.2599, cbr(-2) = -
1.2599
AiryB(x)
R
Airy function Bi(x)
argument (in radian) x≠ k*π/2 with k =
±
1,
±
2…
Mean(a,b,...)
R M
Arithmetic mean
mean(8,9,12,9,7,10) = 9.1666
Meanq(a,b,...)
R M
Quadratic mean
meanq(8,9,12,9,7,10) = 9.300
Meang(a,b,...)
R M
Arithmetic mean
meang(8,9,12,9,7,10) = 9.035
Var(a,b,...)
R M
Variance
var(1,2,3,4,5,6,7) = 4.6666
Varp(a,b,...)
R M
Variance pop.
varp(1,2,3,4,5,6,7) = 4
Stdev(a,b,...)
R M
Standard deviation
Stdev(1,2,3,4,5,6,7) = 2.1602
Stdevp(a,b,...)
R M
Standard deviation pop.
Stdevp(1,2,3,4,5,6,7) = 2
Step(x,a)
R
Haveside's step function
Returns 1 if x ≥ a , 0 otherwise
DSBeta(x, a, b, [j])
R
Beta distribution (j=1 cumulative)
0 < x < 1 , a > 0, b > 0,
DSBinomial(k, n, p, [j])
R
Binomial distribution (j=1 cumulative) k integer, n integer , 0 < p < 1
DSCauchy(x, m, s, n, [j])
R
Cauchy (generalized) distribution (j=1
cumul.)
n integer , s > 0
DSChi(x, r, [j])
R
Chi distribution (j=1 cumulative)
r integer, x > 0
DSErlang(x, k, l, [j]))
R
Erlang distribution (j=1 cumulative)
k integer, x > 0
DSGamma(x, k, l, [j]))
R
Gamma distribution (j=1 cumulative)
x > 0, k > 0, l > 0
DSLevy(x, l, [j]))
R
Levy distribution (j=1 cumulative)
x > 0, l > 0
DSLogNormal(x, m, s, [j]))
R
Log-normal distribution (j=1
cumulative)
x > 0, m ≥ 0, s > 0
DSLogistic(x, m, s, [j]))
R
Logistic distribution (j=1 cumulative)
x > 0, m ≥ 0, s > 0
DSMaxwell(x, a, [j]))
R
Maxwell-Boltzman distribution (j=1
cumulative)
x > 0, a > 0
DSMises(x, k, [j]))
R
Von Mises distribution (j=1
cumulative)
k > 0, -π < x < π
DSNormal(x, m, s, [j]))
R
Normal distribution (j=1 cumulative)
s > 0
DSPoisson(k, z, [j]))
R
Poisson distribution (j=1 cumulative)
k integer, z > 0
DSRayleigh(x, s, [j]))
R
Rayleigh distribution (j=1 cumulative)
x > 0, s > 0
DSRice(x, v, s, [j]))
R
Rice distribution (j=1 cumulative)
x > 0, v ≥ 0 , s > 0
DSStudent(t, v, [j]))
R
Student distribution (j=1 cumulative)
v integer degree of freedom
DSWeibull(x, k, l, [j]))
R
Weibull distribution (j=1 cumulative)
x > 0, k integer, l > 0
Symbol "!" is the same as "Fact", symbol "\" is the integer division, symbols “|x|” is the same as Abs(x)
Logical function and operators returns 1 (true) or 0 (false)
Note: the arguments separator of the functions changes automatically from "," to ";" if your system decimal separator is
comma ",".
