You are here:

Advanced Math/Taylor Series

Advertisement

Expert: - 5/19/2008


Question

function
Hello!
I don't know how I'm supposed to make sum formula from function:
f(x)=e(^x^2)+1)  X0=0(I added in attachment the formula in normal way because this way it seemed lame for me)
How much I understand I'm supposed to make derivatives and than sum them. So far it is ok. But how I understand I have to work out general formula... and that is the problem. I know it is somehow connected with MCLoren's (Tailor's special occasion, when x0=0) row (I hope I spelled it correctly. The professor mentioned it, when I asked.)
With hope for some peace of advice, Liva
PS sorry for my English

Answer
Questioner:   Liva
Category:  Advanced Math
Private:  No
 
Subject:  function_sum_formula
Question:  

functionHello!
I don't know how I'm supposed to make sum formula from function:
f(x)=e(^x^2)+1)  X0=0(I added in attachment the formula in normal way because this way it seemed lame for me)
How much I understand I'm supposed to make derivatives and than sum them. So far it is ok. But how I understand I have to work out general formula... and that is the problem. I know it is somehow connected with MCLoren's (Tailor's special occasion, when x0=0) row (I hope I spelled it correctly. The professor mentioned it, when I asked.)
With hope for some peace of advice, Liva
PS sorry for my English  
.......................
Hi, Liva,

Your idea is good -- write:

e^(x^2 + 1) = e * e^(x^2)

Now you can look up the basic Maclauren series for e^t:
(find it in any calculus book)

e^t = 1 + t + t^2/2! + t^3/3! + ...

or, in summation form:

e^t = SUM[k=0 to inf] t^k/k!

Now do two things:

A. Put t = x^2, and you have:

e^(x^2) = SUM[..] x^2k/k!

B. Multiply each term by  e:

e e^(x^2) = SUM[..] ex^2k/k!

e^(x^2 + 1) = SUM[..] ex^2k/k!

And that is your series.  It looks like:

e + ex^2 + ex^4/2! + ex^6/3! + ...

    Questioner's Rating
    Rating(1-10)Knowledgeability = 10Clarity of Response = 10Politeness = 10
    CommentI cuold not whish a better help and asistance!


  • Add to this Answer
  • Ask a Question

Paul Klarreich

Expertise

I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.

Experience

I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.

Education/Credentials
-----------

©2012 About.com, a part of The New York Times Company. All rights reserved.