mathematical constants and functions
-- an overview
IntroductionThe 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.
arcsin, arcsinh, ...instead of
asin, asinh, .... The exponential integral
function is now called Ei
instead of eint. The 2-argument version of
atan representing the polar angle of a complex number is
replaced by the new function arg.CATALAN replaces the function call
catalan() of previous MuPAD versions.arg,
besselI, besselK, besselY, Ci, Ei, lambertV, lambertW, log, and polylog were implemented.