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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

▪ 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
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 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 source 源程序

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

zeta ﻿