What Does exp Mean in Mathematical Expressions?

[cryforhelp104]

Homework Statement

What would "exp" in a question about approximating functions with Taylor Series mean?

Relevant Equations

exp(-ax^2) about the value x = 0 to second order in x

In my introductory modern physics class, I was asked to compute the Taylor Series for exp(-ax^2) about the value x = 0 to second order in x. I am unfamiliar with the what "exp" before the function means, despite having approximated functions with Taylor Series before. I think there was some gap in my previous math class. I'd appreciate a brief explanation (please don't work the problem, just explain the "exp" part)

 

[Frabjous]

It means $e^{-ax^2}$, the exponential function. With this specific argument, it is also known as a Gaussian function (a very useful function).

 

[berkeman]

Homework Statement: What would "exp" in a question about approximating functions with Taylor Series mean?
Relevant Equations: exp(-ax^2) about the value x = 0 to second order in x

In my introductory modern physics class, I was asked to compute the Taylor Series for exp(-ax^2) about the value x = 0 to second order in x. I am unfamiliar with the what "exp" before the function means, despite having approximated functions with Taylor Series before. I think there was some gap in my previous math class. I'd appreciate a brief explanation (please don't work the problem, just explain the "exp" part)

It means $e^{-ax^2}$, the exponential function. With this specific argument, it is also known as a gaussian function.

Welcome to PF, @cryforhelp104 -- Do you have what you need now to actually show some effort on this schoolwork problem of yours?

 

[cryforhelp104]

Thank you! So the question is to compute the Taylor Series for (e^(-ax^2)) about the value x = 0 to second order in x?

 

[haruspex]

Thank you! So the question is to compute the Taylor Series for (e^(-ax^2)) about the value x = 0 to second order in x?

Yes.

 

[Mark44]

A Taylor series in powers of x (expanded about x = 0) is a Maclaurin series. The Maclaurin series for $e^x$ is one of the simplest infinite series, where $e^x = 1 + \frac x 1 + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots$.
Just do a substitution to get the Maclaurin series for $e^{-ax^2}$ for as many terms as are required and you're done.