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mathematical constants and functions

-- an overview

Introduction

The following mathematical constants are pre-defined in MuPAD:

complexInfinity - complex infinity
I - imaginary unit sqrt(-1) (see DOM_COMPLEX for details)
infinity - real positive infinity
undefined - undefined value

The following constants are symbolic representations of special real numbers. Use float to get floating point approximations with the current precision DIGITS.

CATALAN - Catalan constant sum((-1)^i/(2*i+1)^2, i=0..infinity) = 0.9159..
E - Euler number exp(1) = 2.718.. (see exp for details)
EULER - Euler-Mascheroni constant limit(sum(1/i,i=1..n)-ln(n),n=infinity) = 0.5772..
PI - PI = 3.141..

The following mathematical functions are defined in a MuPAD session:

abs - absolute value of a real or complex number
arg - polar angle of a complex number
bernoulli - Bernoulli numbers and polynomials
besselI - modified Bessel functions of the first kind
besselJ - Bessel functions of the first kind
besselK - modified Bessel functions of the second kind
besselY - Bessel functions of the second kind
beta - beta function
binomial - binomial coefficient
ceil - nearest integer in the direction of infinity
Ci - cosine integral function
dilog - dilogarithm function
dirac - Dirac delta function
Ei - exponential integral function
erf - error function
erfc - complementary error function
exp - exponential function
fact - factorial function
frac - fractional part of a number
floor - nearest integer in the direction of -infinity
gamma - gamma function
heaviside - Heaviside step function
igamma - incomplete gamma function
Im - imaginary part of a complex number
lambertV - lower branch of Lambert's W function
lambertW - main branch of Lambert's W function
log - logarithm to an arbitrary base
ln - natural logarithm
max - maximum of real numbers
min - minimum of real numbers
polylog - polylogarithm function
psi - digamma/polygamma function
Re - real part of a complex number
round - rounding to the nearest integer
Si - sine integral function
sign - sign of a real or complex number
sqrt - square root function
trunc - nearest integer in the direction of 0
zeta - Riemann zeta function

Further, the trigonometric functions and hyperbolic functions

cos, cot, csc, sec, sin, tan, cosh, coth, csch, sech, sinh, tanh

and the inverse functions

arccos, arccot, arccsc, arcsec, arcsin, arctan, arccosh, arccoth, arccsch arcsech, arcsinh, arctanh

are implemented.

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