# Function

Usual keywords are lowercase, which are different from uppercase, e.g. sin is different from Sin.

## 1. Classification

1. Math function
1. Standard Function
2. Special Function:
beta binomial ci chi ei eta erf erfc erfi gamma harmonic lerch li loggamma polygamma polylog psi si shi mittag tani zeta
3. Inverse function:
The inverse of trig function is denoted by prefix "a" onto function name, e.g. asin(x) is inverse of sin(x) for sin^-1(x) , other inverse function is denoted by prefix "inverse" onto function name, e.g. inversef(x) is inverse of f(x) for f^-1(x).
4. Calculus function:
lim limit d diff ds dsolve infint infints int integral integrate integrates odetest semid semiint series taylor totald
5. The nth order derivative function:
the 0.5th order derivative of sin(x) is denoted by sin(0.5,x) for sin^((0.5))(x). the nthd() gives the nth derivative formula.
6. Integral function:
Its last letter is "i" for integral, e.g. ei(x) is exp integral of exp(x)/x, tani(x) is tan(x)/x integral.
7. Discrete math function:
difference differences Delta Deltas sum sums sum0n sum1n sum0inf sum1inf infsum partialsum psum infsum1 partialsum1 psum1 recurrence rsolve tosum
8. Conversion function: convert() convert to another form. Or its first two letters are "to", e.g. tosum(x) convert x to sum.
9. Inert function: If add profix "s" to function name, it becomes to inert function, inactivative, e.g. ds(), integrates(). To activate by removing its last letter "s" or by clicking the simplify button.
10. Numeric function: Its first letter is "n" for numeric, e.g. nsum() is numeric sum.
2. Programming function
1. Test function: Its first two letters are "is".
block if for
3. Internal Function - system function in the .class file.
4. External Function - user-defined function in text file, which is auto loaded. You can add your own new function.

## 2. Definition

Clicking or inputing a function enters it to the Calculator, then click the definition buttion to get its definition.

Add or define new function of a single character name by f(x)=sin(x), other new function by ff(x_):=sin(x).

## 4. Usage

It is similar to math function in Java, JavaScript and Maple. See manual.
You can use first function as command and "to" as ",", e.g.
• convert sinh(x) to exp
then hit the button or the ENTER key in your keybord.

## 5. Function source

abs
acos
acosh
acot
acoth
acsc
acsch
arg
asec
asech
asin
asinh
assume
atan
atan2
atanh

beta
binomial

cbrt
ci
cis
combination
conjugate
convert
cos
cosh
csgn

d
def
define
definition
delta
diff
difference
digamma
doublefactorial
ds
dsolve

ei
eta
erf
erfc
erfi
exp
expand
expandexp
expandtrig

factor
factorial
factorialpower
fallingfactorial
For

gamma
gauss
gaussian
gcd

harmonic
has
hypot

If
im
infint
infints
infsum
infsums
int
integral
integrate
integrates
inverse
inversef
inverselaplace
isatom
isconstant
iscomplex
isfloat
iseven
isfree
isfunction
isinteger
isnumber
isodd
isprime

laplace
lg
li
lim
limit
ln
log
log10
loggamma

max
min
mittag

n
nint
nlim
not
nsolve
nsum

odetest

parametricplot
plot
phi
pochhammer
polarplot
polycoff
polygamma
polylog
prime
prod
product
psi
psolve

random
re
recurrence
risingfactorial
rsolve

semid
semiint
series
sgn
sign
si
simplify
sin
sinc
sinh
solve
sqrt
sum

tan
tani
tanh
tangent
taylor
theta
todegree
toexp
togamma
tofactorial
tolog
toint
tosum
toparfrac
topolar
topower