symsum (Symbolic Math Toolbox)

Symbolic summation

Syntax

r = symsum(s)
r = symsum(s,v)
r = symsum(s,a,b)
r = symsum(s,v,a,b)

Description

symsum(s) is the summation of the symbolic expression s with respect to its symbolic variable k as determined by findsym from 0 to k-1.

symsum(s,v) is the summation of the symbolic expression s with respect to the symbolic variable v from 0 to v-1.

symsum(s,a,b) and symsum(s,v,a,b) are the definite summations of the symbolic expression from v=a to v=b.

Examples

The commands

```
syms k n x
symsum(k^2)
```

return

```
1/3*k^3-1/2*k^2+1/6*k
```

symsum(k) returns

```
1/2*k^2-1/2*k
```

symsum(sin(k*pi)/k,0,n) returns

-1/2*sin(k*(n+1))/k+1/2*sin(k)/k/(cos(k)-1)*cos(k*(n+1))-
1/2*sin(k)/k/(cos(k)-1)

symsum(k^2,0,10) returns

```
385
```

symsum(x^k/sym('k!'), k, 0,inf) returns

```
exp(x)
```

Note The preceding example uses sym to create the symbolic expression k! in order to bypass the MATLAB expression parser, which does not recognize ! as a factorial operator.

See Also

findsym, int, syms

sym2poly taylor