mathematical constants and functions
-- an overview
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.
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.