Recent content by loloPF

I am not sure I want to download the file... sorry. But You might want to know that: \frac{d}{dx}(\frac{1}{f^2(x)})=-2\frac{f'(x)}{f^3(x)}

A friend a mine is a researcher in Maths and eventhough he is not a specialist in integration, a friend of his just recognised the function right away! Like: "Hey dude, this looks like K_1(\gamma), one of the modified Bessel function of second kind :cool: "... nevermind. Anyway you can find...

I just found the answer: this integral is well known as the "modified Bessel function of second kind", period.

Thanks JoAuSc, it's a very wise thing to search for simplifications and particular cases. The "rest" is the tough part, though. Anyway, I have the answer! :smile: I just couldn't find it in textbooks but this integral is well known as the "modified Bessel function of second kind". As...

That's where I stand too... noting that given the bounds the first term is zero. I'm trying to crack it with Maple now (o:)shame on me!) but nothing good so far.

hotvette: Now I see what you meant :smile: I am taking that direction. Tom Mattson: Funny you would think of that, I was also looking into finding a differential equation for which "my" integral would be a solution. I'll let you know guys, I've got to break this one!

HallsofIvy: I think that NewScientist meant that eventhough the ball can be assumed to be a point, the batter can not. Therefore, defining the displacement of the batter by that of his center of gravity, the ball might have a slightly different displacement if it was struck and caught at...

Lots of answers, thanks guys! :smile: but still no result :cry: hotvette: I am not sure about this but I'll try. The pain is you have to split the integral because of the term \sqrt{y^2-\gamma^2} Pseudo Statistic: I do not want a numerical result this time... sorry. Tom Mattson: No...

Then dy=\frac{x}{\sqrt{x^2+\gamma^2}}dx and I don't quite see it happening... Can you be more precise?

A vector CAN NOT have a non-zero component and a zero magnitude. Example in a 3D space: Consider a vector \vec{V}=(v_1,v_2,v_3). By definition its magnitude is: \|\vec{V}\|= \sqrt{\vec{V} \cdot \vec{V}} That is \|\vec{V}\|=\sqrt{v_1^2+v_2^2+v_3^2} Because the square of any number is always...

I just can't solve this: I(\gamma)=\int_{-\infty}^{\infty} e^{-\sqrt{x^2+\gamma^2}}dx I have tried a trigonometric substitution x=\gamma \tan(\theta) but I am not happy with the result . Anyone got a hint?

HallsofIvy, you might have missed the square root in the definition of f: f(X,Y)=\sqrt{a(cY+X)^2+b(cY-X)^2} Definition: I(X)=\int_{-\infty}^{\infty} e^{-f(X,Y)}dY Changes of variable: first u=cY+X then v=u\sqrt{a+b} and w=v-\frac{2bX}{\sqrt{a+b}} leading to...

You are right HallsofIvy and the answer to your question is: "No I do not.", this is why my second point starts with: "and/or [...]". I have made some (but little) progress on this and I'll let you know in a comming post where I stand now.

Funky integral! This integral is driving me nuts :cry: , anyone got a clue? Given two real variables X and Y, one defines the function: f(X,Y)=sqrt(a*(X+cY)^2+b*(X-cY)^2) where a, b and c are reals and a>0, b>0. Then the function g is defined as: g(X,Y)=exp(-f(X,Y)) I am looking for: 1-...

need "gauss like" PDF with skewness I am looking for a Probability Density Function that has the following properties: is defined on R like the gaussian has a non null (and non constant) skewness that is controlled by a parameter degenerates towards the gaussian At the moment I am...