Summary of Math Library v3.02 for NOS 2.x 1. General Math 1.1 Numbers e The natural number. 2.71828182846 euler The Euler-Mascheroni number. 0.577215664902 i The positive square root of negative one. i infinite The largest number for NOS 2^1024. pi The circle ratio. 3.14159265359 primes Table of the first 2585 prime numbers 1.2 General Math Routines Name Ability Description ________________ ______ ____________________________ |+| C M R P Adds two numbers |-| C M R P Subtracts a number from another |*| C M R P Multiplies two numbers |/| C M R Divides one number into another |=| C M R P Tests two numbers for equality |<>| C M R P Tests two numbers for inequality abs C M R Magnitude of a number acos C M R Arccosine of a number acosh C M R Hyperbolic arccosine of a number AirySolution C R Airy solution to Bessel's Equation ArrayAve C M R Arithmetic average of array ArrayMax M R Maximum in array ArrayMin M R Minimum in array ArrayRemoveDuplicates C M R Removes duplicates from array asin C M R Arcsine of a number asinh C M R Hyperbolic arcsine of a number AssocLegendre C R Associated Legendre functions atan C M R Arctangent of a number atan2 C M R Arctangent of a y/x in correct quadrant atanh C M R Hyperbolic arctangent of a number BaseConv M R Converts to and from base 10 BernoulliNumber Bernoulli number BernoulliPolynomial C R Bernoulli function at a number Bessel C R Bessel Function BesselSolution C R Bessel and Neumann solution w/derivs Beta C M R Beta function BinCoeff C M R Binomial Coefficient ChebyshevDerivative R Derivative of Chebyshev polynomial ChebyshevEval R Chebyshev polynomial evaluation ChebyshevFit R Chebyshev polynomial function approximation ChebyshevIntegral R Integral of Chebyshev polynomial CleanComplex C M R Returns real if z.i=0 Cos C M R Cosine of a number Cosh C M R Hyperbolic cosine of a number Cross C R Cross product of three-vector Curl Curl of vector of functions Derivative C M P Derivative of function at value DirichletBeta C M R Infinite power sum Beta DirichletEta C M R Infinite power sum Eta DirichletLambda C M R Infinite power sum Lambda Divergence Divergence of vector of functions Erf C M R Error function, corrects a NOS 2.0 error ErfC C M R Complimentary Error function EulerNumber Euler number EulerPolynomial C R Euler function at a number Exp C M R Exponential of a number fabs C M R Magnitude of a number Factorial C M R Factorial function FloorMod Subtracts until in range Gamma C M R Gamma function GaussJordan C M R Simulataneous equations solving Gradient Gradient of a function HankelSolution C R Hankel solution to Bessel's Equation IncompleteBeta R Incomplete Beta function IncompleteGamma R Incomplete Gamma function Infimum Minimum of function in range Integral M P Integral of function between range IsComplex C M R Tests if a number is a complex type IsHermitian C M R Tests if a matrix is Hermitian IsOrthogonal C M R Tests if a matrix is orthogonal IsRational C M R Tests if a number is a fraction IsSymmetric C M R Tests if a matrix is symmetric IsSkewSymmetric C M R Tests if a matrix is skew symmetric IsUnitary C M R Tests if a matrix is Unitary Laplacian R Laplacian differential operator LBeta C M R Log of Beta function LBinCoeff C M R Log of BinCoeff function LegendrePolynomial C R Legendre polynomials LGamma C M R Log of Gamma function LinearRegression C M R General Linear Regression of paired data Log C M R Natural log of a number LUDecomp C M R Lower-Upper decomposition of matrix LUBacksub C M R LU backsubstitution equation solving MakeComplex C M R Use this to make a complex MakePolynomial C M R Use this to initialize a polynomial MakeRational M Use this to make a rational number ModifiedBessel C R Modified Bessel Function ModifiedNeumann C R Modified Neumann Function ModifiedBesselSolution C R Modified Bessel,Neumann w/derivatives Negate C M R Negates a number Neumann C R Neumann function PFE P Polynomial fraction expansion PiDigit Pi digit extraction for various bases PolyGamma C R Derivatives of LGamma PolyLogMod C R Modulus of PolyLog function PolyNom C M R Evaluates polynomial at a number PolynomialFit C R Fit x and y data to any polynomial PolynomialToChebyshev R Converts polynomial to Chebyshev polynomial PolynomialZeroes C R Zeroes of a polynomial Pow C M R Power PowMod C R Modulus of Pow function QGaussIntegral Gauss-Legendre Quadrature integration ReduceRational M R Reduce rational to smallest fraction RemQuo C R P Remainder and quotient of a division RiemannSiegelTheta C R Riemann-Siegel Theta function RiemannSiegelZ C R Riemann-Siegel Z function RiemannZeta C R Riemann Zeta function RootSearch C Finds the anser to transcendental equations Round C M R Rounds to the nearest integer RoundDec C M R Rounds at a decimal place RoundSigFigs C M R Rounds to some number of significant figures Sin C M R Sine of a number Sinh C M R Hyperbolic sine of a number SinSeries C M R sine series summation SphericalBessel C R Spherical Bessel Function SphericalNeumann C R Spherical Neumann Function SphericalBesselSolution C R Spherical Bessel,Neumann w/derivatives Sqrt C M R Square root of a number Square C M R Square of a number Supremum Maximum of function in range SVDecomp C M R Singular Value decomposition of matrix SVBacksub C M R SV backsubstitution equation solving SymbolicDerivative M R P Symbolic derivative SymbolicIntegral M R P Symbolic integral SymbolicEval M R P Evaluation of function objects Tan C M R Tangent of a number Tanh C M R Hyperbolic tangent of a number UnitNormal Unit normal vector for a function note: Functions will handle C = Complex, M = Matrix, R = Rational, P = Polynomial 2. Statistical Routines 2.1 General Statistical routines Name Description _________ ____________________________ SUniform standard Uniform random number generator SNormal standard Normal random number generator SGamma standard Gamma random number generator Choose picks N numbers from a set of numbers Arrangements finds how many arrangements EstimateMode estimates the distibution peak from data EstimateMedian estimates the distibution median from data EstimateDiscreteness estimates the discreteness of the data EstimateProbability estimates the probability at each data point EstimateCumulation estimates the cumulation at each data point 2.2 Distribution properties Name Description _________ ____________________________ name name of the distribution type 'continuous or 'discrete range the normalized range where the distribution is valid 2.3 Distribution functions Name Description _________ ____________________________ Test tests data for fitness GroupPick picks N numbers from distribution NotWithinRange tests a number if within range Normalize normalizes a number Unnormalize reverses normalization of a number CheckParameters tests parameters if valid Generator generates a random number for distribution Probability probability function Cumulation cumulative function InverseCumulation inverse of Cumulative function Mean Expectation value Median median value Mode peak of distribution StandardDeviation standard deviation Estimator estimates parameters from data Hazard hazard function at a number 2.4 Continuous Distributions Name Alternate Name _________ ____________________________ Beta Cauchy ChiSquared Delta Dirac Delta Exponential Gamma Gumbel Extreme-value Logistic LogNormal MassiveBoson Bose-Einstein (1/2) MassiveFermion Fermi-Dirac (1/2) MasslessBoson Bose-Einstein (2) MasslessFermion Fermi-Dirac (2) Maxwell Normal Gaussian Pareto PT5 Pearson Type V, Inverted Gamma PT6 Pearson Type VI Rayleigh Snedecor Snedecor's F Student Student's t Uniform vonMises Weibull 2.5 Discrete Distributions Bernoulli Binomial DiscreteUniform Geometric Hypergeometric Logarithmic NegativeBinomial Poisson