Mathematical Analysis

David8765

New member
Joined
Jun 5, 2019
Messages
4
1246512466
I need help to proof how the series meets the equation
 

mmm4444bot

Super Moderator
Staff member
Joined
Oct 6, 2005
Messages
10,302
Please follow the forum's submission guidelines and post what you've tried or thought about so far. Thank you.

\(\;\)
 

topsquark

Full Member
Joined
Aug 27, 2012
Messages
382
I'll start you off, though, in case you are having trouble starting it. What are f'(x) and f''(x)?

-Dan
 

Anthobet

New member
Joined
May 27, 2019
Messages
5
I'll start you off, though, in case you are having trouble starting it. What are f'(x) and f''(x)?

-Dan
I also think you can simplify the summation using some arithmetic and a Maclaurin Series identity.
 

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
18,354
I also think you can simplify the summation using some arithmetic and a Maclaurin Series identity.
Can you calculate f'(x) and f"(x) for the given function?

To start off what is the first derivative of x2n?
 

David8765

New member
Joined
Jun 5, 2019
Messages
4

pka

Elite Member
Joined
Jan 29, 2005
Messages
8,241
\(\displaystyle \begin{align*}y &= \sum\limits_{n = 0}^\infty {\frac{{{{( - 1)}^n}{x^{2n}}}}{{{2^{2n}}{{(n!)}^2}}}} \\
y' &= \sum\limits_{n = 0}^\infty {\frac{{{{( - 1)}^n}n{x^{2n - 1}}}}{{{2^{2n - 1}}{{(n!)}^2}}}} \end{align*}\)
 

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
18,354
Can you calculate f'(x) and f"(x) for the given function?

To start off what is the first derivative of x2n?
Look at pka's answer in response #9.

Now tell us:

what would be the expression for f"(x) - or y"?
 
Top