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# 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:
B Beta beta binomial
Cl Clausen ci chi
dilog digamma doublefactorial
Ei Ein En eta erf erfc erfi
factorial fallingfactorial
Gamma gamma gaussi
H harmonic
lerch li loggamma
Phi pochhammer polygamma polylog psi
si shi smallgamma
mittag
tani
zeta
3. Inverse function:
If add prefix "inverse" to function name, it becomes to the inverse function, e.g. inversef(x) is inverse of f(x) for f^-1(x). 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.
4. to function:
If add prefix "to" to function name, it becomes to the convert function, e.g. adding prefix "to" to sin(x) becomes tosin(x), tosin convert x to sin. Or use convert() function convert to another form. e.g. convert exp(x) to sin
5. Integral function:
If add profix "i" to function name, it becomes to the integral function. Its last letter is "i" for integral, e.g. adding profix "i" to tan become tani, tani(x) is integral of tan(x)/x.
6. Inert function:
If add profix "s" to function name, it becomes to the inert function. Its last letter is "s" for inactivative, e.g. ds(), integrates(). A non-integer derivative is inert, e.g. sin^((0.5))(x), to activate by removing its last letter "s" or by clicking the simplify button.
7. Calculus function:
lim limit d diff ds dsolve infint int integral integrate integrates odetest semid semiint series taylor totald
8. The nth order derivative function:
The nthd() gives the nth derivative formula. It is symbolic higher derivative. The 0.5th order derivative of sin(x) is denoted by sin(0.5,x) for sin^((0.5))(x). The minus order derivative is intergal, e.g. sin^((-1))(x) is int sin(x), it is different from sin^-1(x), which is inverse of sin(x). A non-integer derivative is inert, e.g. sin^((0.5))(x), to activate by clicking the evaluate button.
9. Discrete math function:
difference differences Delta sum sums sum0n sum1n sum0inf sum1inf infsum partialsum psum infsum1 partialsum1 psum1 recurrence rsolve tosum
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". e.g. isreal().
block if for While
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 Gamma(x) to x!
then hit the button or the ENTER key in your keybord.

## 5. Function source

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

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