#### Constants

• Boltzmann() = 1.3806504e-23 J / degK
• CLight() = 299792458.0 m/s (speed of light)
• euler() = 0.5772156649015328606065120900824024310422
• 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
• pi() = 3.1415926535897932384626433832795028841972
• Planck() = 6.62606896e-34 kg m^2 / s (Planck's constant)
• StefanBoltzmann() = 5.670400e-8 W m^2 / degK^4

#### Basic Functions

• abs(x) = absolute value of x
• ceil(x) = round x up to nearest integer
• exp(x) = exponential of x
• floor(x) = round x down to nearest integer
• int(x) = round x down to nearest integer
• 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
• mod(x, y) = floating point remainder of y / x
• 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
• round(x) = round x to nearest (up or down) integer
• sign(x) = sign of x
• sqrt(x) = square root of x

#### Trigonometric Functions

• acos(x) = arccosine of x
• acot(x) = arccotangent of x
• acsc(x) = arccosecant of x
• 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
• cos(x) = cosine of x
• cosh(x) = hyperbolic cosine of x
• cot(x) = cotangent of x
• coth(x) = hyperbolic cotangent of x
• csc(x) = cosecant of x
• csch(x) = hyperbolic cosecant of x
• sec(x) = secant of x
• sech(x) = hyperbolic secant of x
• sin(x) = sine of x
• sinh(x) = hyperbolic sine of x
• tan(x) = tangent of x
• tanh(x) = hyperbolic tangent of x

• AiryAi(x) = Airy function Ai(x)
• AiryBi(x) = Airy function Bi(x)
• 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)
• 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)
• Erf(x) = error function
• Erfc(x) = complimentary error function
• ExpInt(x) = exponential integral E(1, x)
• ExpIntEi(x) = exponential integral Ei(x)
• ExpIntN(n, x) = exponential integral E(n, x)
• 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)
• IncBetaFunc(a, b, x) = incomplete Beta function I(a, b, x)
• 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)
• LogGammaFunc(x) = natural log of the gamma function of x

#### Vector Functions

• angle(x, y) = angle between vectors x and y
• component(x, n) = the nth componet of a vector x
• cross(x, y) = cross product of vectors x and y
• dot(x, y) = dot product of vectors x and y
• mag(x) = magnitude of vector x
• PolarAngle(x) = atan2(x, x) = atan2(component(x, 2), component(x, 1))
• PolarVec(f, q) = [cos(q), sin(q), 0] * f

#### Functions of User-Defined Functions

• fmax(y, x1, x2, ...) = choose x1, x2, ... to maximize y
• fmin(y, x1, x2, ...) = choose x1, x2, ... to minimize y
• func(x1, val1, x2, val2, ...) = evaluate func(x1 = val1, x2 = val2, ...)
• solve(y1, y2, ..., x1, x2 ... ) = choose x1, x2, ... such that y1 = y2 = ... 0

#### Other Functions

• BEGIN = marks the start of a user-defined function
• cgs(e1, e2, ...) = use centimeter-gram-second default units with exceptions e1, e2, ... (args are optional)
• DefUnit(name, x) = user defined unit 'name' set = x
• END = marks the end of a user-defined function
• FPS(e1, e2, ...) = use Foot-Pound-Second default units with exceptions e1, e2, ... (args are optional)
• IPS(e1, e2, ...) = use Inch-Pound-Second default units with exceptions e1, e2, ... (args are optional)
• MKS(e1, e2, ...) = use Meter-Kilogram-Second default units with exceptions e1, e2, ... (args are optional)
• PrintFunc = print the currently defined user-function