Multiplication of two Taylor series

**macca101** · July 15th 2006, 06:16 AM

I'm trying to multiply two Taylor series together to find the quartic Taylor polynomial about 0 of a function

$ (1+\frac{1}{2}x^2+\frac{1}{6}x^3+....)(x-\frac{1}{2}x^2+\frac{1}{3}x^3-...) $

$ = 1(x-\frac{1}{2}x^2+\frac{1}{3}x^3-...)+\frac{1}{2}x^2(x-\frac{1}{2}x^2+...)+\frac{1}{6}x^3(x-...) $

$ = x+(-\frac{1}{2})x^2+(\frac{1}{3}+\frac{1}{2})x^3+(-\frac{1}{4}+\frac{1}{6})x^4 $

$ = x-\frac{1}{2}x^2+\frac{5}{6}x^3-\frac{1}{12}x^4 $

The problem is when I enter the function into my computer maths program(mathcad) I get.

$ = x-\frac{1}{2}x^2+\frac{5}{6}x^3-\frac{1}{3}x^4 $

where am I going wrong

Oh the function by the way is

$ f(x)= (e^x-x)(\ln(1+x)) $

**galactus** · July 15th 2006, 06:58 AM

Originally Posted by macca101

I'm trying to multiply two Taylor series together to find the quartic Taylor polynomial about 0 of a function

$ (1+\frac{1}{2}x^2+\frac{1}{6}x^3+....)(x-\frac{1}{2}x^2+\frac{1}{3}x^3-...) $

$ = 1(x-\frac{1}{2}x^2+\frac{1}{3}x^3-...)+\frac{1}{2}x^2(x-\frac{1}{2}x^2+...)+\frac{1}{6}x^3(x-...) $

$ = x+(-\frac{1}{2})x^2+(\frac{1}{3}+\frac{1}{2})x^3+(-\frac{1}{4}+\frac{1}{6})x^4 $

$ = x-\frac{1}{2}x^2+\frac{5}{6}x^3-\frac{1}{12}x^4 $

The problem is when I enter the function into my computer maths program(mathcad) I get.

$ = x-\frac{1}{2}x^2+\frac{5}{6}x^3-\frac{1}{3}x^4 $

where am I going wrong

Oh the function by the way is

$ f(x)= (e^x-x)(\ln(1+x)) $

You're missing a -1/4 term

-1/4-1/4+1/6=-1/3

$x-\frac{x^{2}}{2}+\frac{x^{3}}{3}-\frac{x^{4}}{4}+\frac{x^{3}}{2}-\frac{x^{4}}{4}+\frac{x^{4}}{6}=x-\frac{x^{2}}{2}+\frac{5x^{3}}{6}-\frac{x^{4}}{3}$

**macca101** · July 15th 2006, 07:35 AM

Originally Posted by galactus

[b]You're missing a -1/4 term

Of course I am

Thanks

Thread: Multiplication of two Taylor series

LinkBack

Thread Tools

Display

Multiplication of two Taylor series

Similar Math Help Forum Discussions

Multiplication of series

Multiplication of Taylor series

Multiplication of Two series.Anyone?

question about power series, taylor series, maclaurin series

Using elementary taylor series for taylor polynomial

Search Tags