The nth derivative of 1/(x^2+a^2)

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NicolasLegnazzi

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Hello, I am a physics student, I am looking for the nth derivative respect "a" of the following function:

[MATH]\frac{\partial^n}{\partial^na}(\frac{1}{(x^2+a^2)})[/MATH] Where "a" is real


I know there is a way to solve it using complex analysis. Could you give me a hand?
 
1) What are the first two such partial derivatives?
2) You may wish to consider a series expansion of your expression.
3) Is "a" a Real NUMBER? What's [math]\dfrac{d}{d3}\;3[/math]? In other words, are we SURE we know what we're asking?

Perhaps some additional context and a demonstration of your personal efforts will clear up some confusion.
 
tkhunny said:
1) What are the first two such partial derivatives?
2) You may wish to consider a series expansion of your expression.
3) Is "a" a Real NUMBER? What's [math]\dfrac{d}{d3}\;3[/math]? In other words, are we SURE we know what we're asking?

Perhaps some additional context and a demonstration of your personal efforts will clear up some confusion.
Click to expand...
I am looking to compute that derivative numerically, "a" is a real variable. It does not matter if the solution is expressed in an expansion
 
NicolasLegnazzi said:
Hello, I am a physics student, I am looking for the nth derivative respect "a" of the following function:
[MATH]\frac{\partial^n}{\partial^na}(\frac{1}{(x^2+a^2)})[/MATH] Where "a" is real
I know there is a way to solve it using complex analysis. Could you give me a hand?
Click to expand...
It derivative with respect to \(a\) is the same as respect to \(x\). Just swap variables.
Look at THIS.
 
NicolasLegnazzi said:
But I look for the formula for the nth derivative
Click to expand...
Well do the messy calculations. Don't expect us to do your work for you.
I posted a link to the fifth derivative. What one does is to do a series of derivatives.
Look for a pattern. Then generalize.
 
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