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development of a function and set of convergence

0

$begingroup$

I want to find the development of the function $ e^{x^2}$
and the set of convergence.

Considering that:
$e^x= sum_{k=0}^n frac {x^k}{k!} + R_n(x,0)$

and substituting $x$ with $x^2$ I can write
$e^{x^2}= sum_{k=0}^n frac {x^{2k}}{k!} + R_n(x,0)$

Now I have to prove that $ R_n(x,0)$ tends to $0$ to say that

$e^{x^2}= sum_{k=0}^infty frac {x^{2k}}{k!}$

and for which $x$ it happens.

please help me

sequences-and-series analysis taylor-expansion

share|cite|improve this question

asked Mar 22 at 12:21

AnneAnne

797419

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It is $R_n(x^2, 0)$ after the substitution ...
  $endgroup$
  – Martin R
  Mar 22 at 12:26
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  ok , and if I had $R(x,x_0)$, does it become $R(x^2, {x_0}^2)$?
  $endgroup$
  – Anne
  Mar 22 at 12:29
  
  
  

  
  
  
  

add a comment | 

0

$begingroup$

I want to find the development of the function $ e^{x^2}$
and the set of convergence.

Considering that:
$e^x= sum_{k=0}^n frac {x^k}{k!} + R_n(x,0)$

and substituting $x$ with $x^2$ I can write
$e^{x^2}= sum_{k=0}^n frac {x^{2k}}{k!} + R_n(x,0)$

Now I have to prove that $ R_n(x,0)$ tends to $0$ to say that

$e^{x^2}= sum_{k=0}^infty frac {x^{2k}}{k!}$

and for which $x$ it happens.

please help me

sequences-and-series analysis taylor-expansion

share|cite|improve this question

asked Mar 22 at 12:21

AnneAnne

797419

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It is $R_n(x^2, 0)$ after the substitution ...
  $endgroup$
  – Martin R
  Mar 22 at 12:26
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  ok , and if I had $R(x,x_0)$, does it become $R(x^2, {x_0}^2)$?
  $endgroup$
  – Anne
  Mar 22 at 12:29
  
  
  

  
  
  
  

add a comment | 

$begingroup$

I want to find the development of the function $ e^{x^2}$
and the set of convergence.

Considering that:
$e^x= sum_{k=0}^n frac {x^k}{k!} + R_n(x,0)$

and substituting $x$ with $x^2$ I can write
$e^{x^2}= sum_{k=0}^n frac {x^{2k}}{k!} + R_n(x,0)$

Now I have to prove that $ R_n(x,0)$ tends to $0$ to say that

$e^{x^2}= sum_{k=0}^infty frac {x^{2k}}{k!}$

and for which $x$ it happens.

please help me

sequences-and-series analysis taylor-expansion

share|cite|improve this question

asked Mar 22 at 12:21

AnneAnne

797419

$endgroup$

share|cite|improve this question

asked Mar 22 at 12:21

AnneAnne

797419

share|cite|improve this question

asked Mar 22 at 12:21

AnneAnne

797419

asked Mar 22 at 12:21

AnneAnne

797419

asked Mar 22 at 12:21

AnneAnne

797419