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Function 函数

Function Theory 函数论

二级学科, 专业名称:函数论, 门类/类别:理学     学科/类别:数学

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

Classification 分类


▪ 4110:实变函数论   ▪ 4120:单复变函数论   ▪ 4130:多复变函数论   
▪ 4140:函数逼近论   ▪ 4150:调和分析       ▪ 4160:复流形   
▪ 4170:特殊函数论   ▪ 4199:函数论其他学科    
  1. Math function 数学函数
    1. Standard Function 初等函数
    2. Special Function 特殊函数
      B Beta beta binomial
      C Cl Clausen ci chi
      dilog digamma doublefactorial
      E Ei Ein En eta erf erfc erfi
      factorial fallingfactorial
      Gamma gamma gaussi
      H harmonic
      L lerch li loggamma
      P Phi pochhammer polygamma polylog psi
      S si shi smallgamma
    3. Inverse function 反函数
      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. 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.
    6. Calculus function 微积分函数
      lim limit d diff ds dsolve infint int integral integrate integrates odetest semid semiint series taylor completed
    7. The nth order derivative function 导数
      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 simplify button.
    8. Integral function 积分函数
      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.
    9. Discrete math function 离散数学
      difference differences Delta sum sums sum0n sum1n sum0inf sum1inf infsum partialsum psum infsum1 partialsum1 psum1 recurrence rsolve tosum
    10. Numeric function 计算数学
      Its first letter is "n" for numeric, e.g. nsum() is numeric sum.
  2. plot function 制图函数
    plot(x), implicitplot(x=y), parametricplot(x,y), tangentplot(x), secantplot(x), polarplot(x), plot3d()
    制图, 隐函数制图, 参数制图, 切线制图, 割线制图, 极坐标制图, 立体图
  3. geometry function 几何函数
    semicircle(r), circle(r), oval(rx,ry), tangent(x)
  4. animation function 动画函数
    timer(4), sinwave(4), sunrise(4)
  5. Programming function 编程函数
    1. "is" function: Its first two letters are "is". e.g. isreal(), isnumber(), isconctant()
    2. condition function : if()
    3. repeat function : for() While()
    4. block()
  6. Internal Function 内部函数
    system function in the Java API.
  7. External Function 外部函数
    user-defined function in text .txt file, which is auto loaded. You can add your own new function.
  • Add New Function 添加新函数

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

    Clicking or inputing a function enters it to the Calculator, then click the definition buttion to get its definition.
  • Usage 使用方法

    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.


  • Function Graph 函数图

  • List of Function 函数表

  • Function source 源程序

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

    B Beta beta binomial block

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

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

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

    factor factorial factorialpower fallingfactorial floor For for FresnelC FresnelS

    Gamma gamma GammaQ gammaP 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

    L laplace lasolve left Lerch lg li lim limit ln log log10 loggamma

    max min mittag mod modInverse

    n nextprime nint nlim not nsolve nsum nthd


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

    random re recurrence remainder replace right risingfactorial rsolve round

    S 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 topolyroot topower tosin tosinh toradian totrig totrigh totald trigamma type


    when While


    See Also