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Function Theory 函数论

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

Classification 分类

三级学科

1. Math function 数学函数
   1. Standard Function 初等函数
      Basic Functions Logarithmic Functions Circular Functions Hyperbolic Functions Miscellaneous Functions

   2. Special Function 特殊函数
      Gamma Functions Bessel Functions Orthogonal Polynomials Elliptic Integrals Elliptic Functions Hypergeometric Functions Zeta Functions

      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
      mittag
      tani
      zeta

   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 数值函数 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.