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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.

3. Add New Function

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.

    convert
    dsolve
    gamma

    5. Function source

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

    B Beta beta binomial block

    cbrt ceil ci circle cis Cl Clausen chi combination conjugate convert cos cosh csc csch csgn

    d def define definition delta diff difference digamma dilog doublefactorial ds dsolve

    E1 Ei Ein En evaluate eta erf erfc erfi exp expand expandexp expandtrig

    factor factorial factorialpower fallingfactorial floor For for FresnelC FresnelS

    Gamma gamma gauss gaussi gaussian gcd gsolution

    H harmonic has hypot

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

    laplace left lerch lg li lim limit ln log log10 loggamma

    max min mittag mod

    n nextprime nint nlim not nsolve nsum nthd

    odetest

    Phi parametricplot partialsum plot pochhammer polar polarplot poly polycoff polygamma polylog point prime prod product psi psolve psolution psum

    random re recurrence replace right risingfactorial rsolve round

    sec sech secantplot semid semiint series sgn sign si simplify sin sinc sinh smallgamma solve Sophomore sqrt sum sum0inf sum0n sum1inf sum1n swap

    tan tani tanh tangent tangentplot taylor theta tocomplex tocos tocosh todegree toerf toexp togamma tofactorial tolog toint tointegral tosum toparfrac topolar topoly topower tosin tosinh toradian totrig totrigh totald trigamma type

    value

    when While

    zeta

    


    See Also


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