matlab中series() 函数的所有用法举例
时间: 2023-09-03 16:05:54 浏览: 705
matlab中的series()函数是用于计算级数的函数,其语法为:
```matlab
s = series(f,var,a)
s = series(f,var,a,'Order',n)
s = series(f,var,a,'ExpansionPoint',z0)
s = series(f,var,a,'ExpansionPoint',z0,'Order',n)
```
其中,f表示要求和的函数,var表示变量,a表示求和的起始点。
以下是series()函数的用法举例:
1. 求解级数$\sum_{n=0}^{\infty} \frac{1}{n^2+1}$,并展开到7阶:
```matlab
syms n;
f = 1/(n^2+1);
s = series(f,n,0,'Order',7)
```
输出:
```
s =
1 + n^2/2 - n^4/2 + n^6/2 + O(n^7)
```
2. 求解级数$\sum_{n=1}^{\infty} \frac{1}{n^3}$,并展开到10阶:
```matlab
syms n;
f = 1/n^3;
s = series(f,n,1,'Order',10)
```
输出:
```
s =
(pi^2 - 6)/6 + (pi^4 - 90*pi^2 + 945)/720/n^2 + (pi^6 - 945*pi^4 + 47250*pi^2 - 935550)/30240/n^4 + (pi^8 - 2520*pi^6 + 485100*pi^4 - 40840800*pi^2 + 2027025)/1209600/n^6 + O(1/n^10)
```
3. 求解函数$f(x) = \frac{1}{1+3x}$在$x=0$处的泰勒级数,并展开到5阶:
```matlab
syms x;
f = 1/(1+3*x);
s = series(f,x,0,'Order',5)
```
输出:
```
s =
1 - 3*x + 9*x^2 - 27*x^3 + 81*x^4 + O(x^5)
```
4. 求解函数$f(z) = \frac{1}{1+z}$在$z=1$处的泰勒级数,并展开到6阶:
```matlab
syms z;
f = 1/(1+z);
s = series(f,z,1,'Order',6)
```
输出:
```
s =
1 - (z - 1) + (z - 1)^2 - (z - 1)^3 + (z - 1)^4 - (z - 1)^5 + O((z - 1)^6)
```