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# Functions Listed Alphabetically

Notes:
(1) Functions are NOT case sensitive (e.g., pi( ) = Pi( ) = PI( )).
(2) Variable names cannot match any function name.

### ABC - DE - FG - KL - MN - PR - Z

#### A

abs(x) = absolute value of x
acos(x) = arccosine of x
acot(x) = arccotangent of x
acsc(x) = arccosecant of x
AiryAi(x) = Airy function Ai(x)
AiryBi(x) = Airy function Bi(x)
angle(x, y) = angle between vectors x and y
asec(x) = arcsecant of x
asin(x) = arcsine of x
atan(x) = arctangent of x
atan2(y, x) = arctangent in correct quadrant of y/x

#### B

BEGIN = marks the start of a user-defined function
BesselI(n, x) = modified Bessel function of the first kind, I(n, x)
BesselJ(n, x) = Bessel function of the first kind, J(n, x)
BesselK(n, x) = modified Bessel function of the second kind, K(n, x)
BesselY(n, x) = Bessel function of the second kind, Y(n, x)
BetaFunc(z, w) = beta function B(z, w)
Boltzmann() = 1.3806504e-23 J / degK

#### C - D

ceil(x) = round x up to nearest integer
cgs(e1, e2, ...) = use centimeter-gram-second default units with exceptions e1, e2, ... (args are optional)
CLight() = 299792458.0 m/s (speed of light)
component(x, n) = the nth componet of a vector x
cos(x) = cosine of x
cosh(x) = hyperbolic cosine of x
cot(x) = cotangent of x
coth(x) = hyperbolic cotangent of x
cross(x, y) = cross product of vectors x and y
csc(x) = cosecant of x
csch(x) = hyperbolic cosecant of x
DefUnit(name, x) = user defined unit 'name' set = x
dot(x, y) = dot product of vectors x and y

#### E - F

EllipticE(phi, k) = Legendre elliptic integral of the second kind, E(phi, k)
EllipticF(phi, k) = Legendre elliptic integral of the first kind F(phi, k)
EllipticPi(phi, n, k) = Legendre elliptic integral of the third kind, Pi(phi, n, k)
END = marks the end of a user-defined function
Erf(x) = error function
Erfc(x) = complimentary error function
euler() = 0.5772156649015328606065120900824024310422
exp(x) = exponential of x
ExpInt(x) = exponential integral E(1, x)
ExpIntEi(x) = exponential integral Ei(x)
ExpIntN(n, x) = exponential integral E(n, x)
floor(x) = round x down to nearest integer
fmax(y, x1, x2, ...) = choose x1, x2, ... to maximize y
fmin(y, x1, x2, ...) = choose x1, x2, ... to minimize y
FPS(e1, e2, ...) = use Foot-Pound-Second default units with exceptions e1, e2, ... (args are optional)
func(x1, val1, x2, val2, ...) = evaluate func(x1 = val1, x2 = val2, ...)

#### G - K

GammaFunc(x) = gamma function of x
GammaPFunc(a, x) = incomplete Gamma function P(a, x)
GammaQFunc(a, x) = incomplete Gamma function Q(a, x) = 1 - P(a, x)
gas() = 8.31434 J / mol / degK = kg m^2 / s^2 degK mol
GEarth() = 6.67428e11 m^3 / kg s^2 (Earth's gravitational constant)
grav() = 9.806652 m / s^2
IncBetaFunc(a, b, x) = incomplete Beta function I(a, b, x)
int(x) = round x down to nearest integer
IPS(e1, e2, ...) = use Inch-Pound-Second default units with exceptions e1, e2, ... (args are optional)
JacobiCN(u, kc) = Jacobian elliptic function, cn(u, kc)
JacobiDN(u, kc) = Jacobian elliptic function, dn(u, kc)
JacobiSN(u, kc) = Jacobian elliptic function, sn(u, kc)

#### L - M

LinInterp(x1, y1, x2, y2, x) = y1 + (x - x1) * (y2 - y1) / (x2 - x1)
ln(x) = natural logarithm of x
log(x) = natural logarithm of x
log10(x) = log base 10 of x
LogGammaFunc(x) = natural log of the gamma function of x
mag(x) = magnitude of vector x
MKS(e1, e2, ...) = use Meter-Kilogram-Second default units with exceptions e1, e2, ... (args are optional)
mod(x, y) = floating point remainder of y / x

#### N - P

Normsdist(z) = standard normal cumulative distribution (mean = 0, stdev = 1)
Normsinv(z) = inverse of the standard normal cumulative distribution (mean = 0, stdev = 1)
Number(x, units) = dimensionless value of x in units
pi() = 3.1415926535897932384626433832795028841972
Planck() = 6.62606896e-34 kg m^2 / s (Planck's constant)
PolarAngle(x) = atan2(x[2], x[1]) = atan2(component(x, 2), component(x, 1))
PolarVec(f, q) = [cos(q), sin(q), 0] * f
PrintFunc = print the currently defined user-function

#### R - Z

round(x) = round x to nearest (up or down) integer
sec(x) = secant of x
sech(x) = hyperbolic secant of x
sign(x) = sign of x
sin(x) = sine of x
sinh(x) = hyperbolic sine of x
solve(y1, y2, ..., x1, x2 ... ) = choose x1, x2, ... such that y1 = y2 = ... 0
sqrt(x) = square root of x
StefanBoltzmann() = 5.670400e-8 W m^2 / degK^4
tan(x) = tangent of x
tanh(x) = hyperbolic tangent of x