Mclauren series for Guassian Integral

  • Thread starter Thread starter soothsayer
  • Start date Start date
  • Tags Tags
    Integral Series
AI Thread Summary
The discussion focuses on finding the Maclaurin series for the Gaussian integral function. The initial confusion about calculating f(0) and subsequent derivatives is resolved by integrating the series for e^-x^2 term-by-term. It is confirmed that f(0) equals zero. The approach involves calculating the derivatives at zero after determining the function. The method effectively simplifies the process of deriving the Maclaurin series for the given function.
soothsayer
Messages
422
Reaction score
5
I'm supposed to be finding the McLauren series for the following function:
latex2png.2.php?z=100&eq=\int_{0}^{x}%20e^{-t^2}dt.jpg


I don't even know where to start... f'(0) is easy to calculate, but what about f(0) and any subsequent derivatives evaluated at 0?
 
Mathematics news on Phys.org
Nevermind! I think I got this, I simply found the series for e^-x^2 and integrated the first few terms term-by-term and found f(x). f(0) was clearly zero. Then I simply did the same thing with the derivative.
 
Thread 'Video on imaginary numbers and some queries'

Thread 'Video on imaginary numbers and some queries'

Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Similar threads

A An interesting series - what does it converge to?
Replies
5
Views
2K
A Can You Prove the Series Is Periodic?
Replies
33
Views
3K
A Expansion with respect to ##z_1##
Replies
1
Views
1K
I Method for finding a complex series?
Replies
10
Views
2K
I What does it mean when an integral is evaluated over a single limit?
Replies
23
Views
5K
I Infinite Series of Infinite Series
Replies
7
Views
2K
I Taylor series to evaluate fractional-ordered derivatives
Replies
3
Views
2K
I Can Taylor series be used to get the roots of a polynomial?
Replies
16
Views
5K
B Periodic smooth alternating series other than sin and cos
Replies
16
Views
3K
I Have you ever used "symbolic logic" to help you learn calculus?
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top