### Related

##### deftaylor-exp-inf-powerseries-sqrt-sum

deftaylor (f(x), x^2 ...

powerseries (f(x), x...

taylor (exp (sqrt (f...

Calculate

##### deftaylor-integrate-powerseries-sum

deftaylor (f(x), sum(...

powerseries (f(x), x,...

taylor (f(x), x, 0, 4);

Calculate

##### deftaylor-inf-sum

deftaylor (f(x), sum(...

taylor (f(x), x, 0, 4);

Calculate

##### deftaylor-powerseries-sum

deftaylor (f(x), sum(...

powerseries (f(x), x,...

taylor (f(x), x, 0, 4);

Calculate

##### deftaylor-powerseries-sum

deftaylor (f(x), sum(...

powerseries (f(x), x,...

taylor (f(x), x, 0, 4);

Calculate

##### deftaylor-inf-sum

deftaylor (f(x), x^2 ...

Calculate

##### deftaylor-integrate-powerseries-sum

deftaylor (f(x), sum(...

powerseries (f(x), x,...

g(x):= taylor (f(x), ...

Calculate

##### deftaylor-inf-powerseries-sum

deftaylor (f(x), sum(...

powerseries (f(x), x,...

g(x):= taylor (f(x), ...

Calculate

##### deftaylor-inf-sum

deftaylor (f(x), x^2 ...

f(x=1);

Calculate

? deftaylor;

Calculate

### deftaylor

Run Example
```(%i1)deftaylor (f(x), cos(x)-cos(y) + sum(x^i/(2^i*i!^2), i, 4, inf));
(%o1)                                 [f]
(%i2) taylor (exp (sqrt (f(x))), x, 0, 4);
%i sqrt(cos(y) - 1)                       2
%i sqrt(cos(y) - 1)   (%e                    sqrt(cos(y) - 1) %i) x
(%o2)/T/ %e                    + ----------------------------------------------
4 cos(y) - 4
%i sqrt(cos(y) - 1)
- (((385 %e                    sqrt(cos(y) - 1) %i
%i sqrt(cos(y) - 1)                 %i sqrt(cos(y) - 1)
+ 576 %e                   ) cos(y) + 191 %e
%i sqrt(cos(y) - 1)   4
sqrt(cos(y) - 1) %i - 576 %e                   ) x )
2
/(18432 cos (y) - 36864 cos(y) + 18432) + . . .
(%i3) ```
Run Example
```deftaylor (f(x), sum( ( ((-1)^n) * (x^(2*n+1)) ) / ((2*n+1)*(2*n+1)!), n, 0, 3));
(%o1)                                 [f]
(%i2) powerseries (f(x), x, 0);
7      5     3
x      x     x
(%o2)                       - ----- + --- - -- + x
35280   600   18
(%i3) g(x):= taylor (f(x), x, 0, 4);
(%o3)                    g(x) := taylor(f(x), x, 0, 4)
(%i4) integrate(g(x),x,0.1);
2    4
x    x
(%o4)                               -- - --
2    72
(%i5) ```
Run Example
```deftaylor (f(x), x^2 + sum(x^i/(2^i*i!^2), i, 4, inf));
(%o1)                                 [f]
(%i2) ```

### Related Help

Help for Deftaylor