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Feb
24
asked Does $\mid x-y\mid>0,x\neq-y$ imply $\mid\mid x\mid-\mid y\mid\mid>0$?
Feb
21
accepted Is the integral of square of a function (with parameter) positive?
Feb
20
asked Is the integral of square of a function (with parameter) positive?
Feb
19
comment Integrate $I=\int_e^\infty\left(\frac{\log\log y}{y(y+1)}\right)^2dy$ using residue calculus?
I actually meant from $1$, not $e $. My mistake.
Feb
19
accepted Integrate $I=\int_e^\infty\left(\frac{\log\log y}{y(y+1)}\right)^2dy$ using residue calculus?
Feb
18
comment Integrate $I=\int_e^\infty\left(\frac{\log\log y}{y(y+1)}\right)^2dy$ using residue calculus?
Oh yes, sorry I missed that.
Feb
18
comment Integrate $I=\int_e^\infty\left(\frac{\log\log y}{y(y+1)}\right)^2dy$ using residue calculus?
Of course - the branch. I wonder If I could create a branch cut along the negative axis and use a half key hole contour... looking at the answer below I doubt it...
Feb
18
comment Integrate $I=\int_e^\infty\left(\frac{\log\log y}{y(y+1)}\right)^2dy$ using residue calculus?
Thanks for the detailed answer.
Feb
17
asked Integrate $I=\int_e^\infty\left(\frac{\log\log y}{y(y+1)}\right)^2dy$ using residue calculus?
Feb
17
comment Can one define a cross product for functions?
If using the analogy with vectors, then maybe such a "cross product function" $c(x)\not\equiv0$ should have the property $$\int_{\mathbb{R}}c(x)(a(x)-b(x))dx=0$$ since for vectors $\mathbf{a}\cdot \mathbf{c}=\mathbf{b}\cdot \mathbf{c}=0$. If you could find such a $c(x)$ for given $a(x)$ and $b(x)$ then you are free to define it.
Feb
16
comment How to approach this integration problem?
Define "draw", "cute", and "bunny". Sorry, couldn't resist.
Feb
16
revised How to solve this DDE: $f'(x-1)-f''(x)=g(x)$.
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Feb
16
revised How to solve this DDE: $f'(x-1)-f''(x)=g(x)$.
edited title
Feb
16
asked How to solve this DDE: $f'(x-1)-f''(x)=g(x)$.
Feb
16
comment Evaluation of Bose-Einstein and Fermi-Dirac Integrals
First thing I'd do is a change of variable $y=(p-\mu)/T$, because in the case of $e^y-1$ in the denominator you will probably end up with the Riemann zeta function $\zeta(\cdot)$. Not totally sure on that one, would have to perform the substitution to be sure, but see en.wikipedia.org/wiki/Riemann_zeta_function#Definition to see what I'm getting at.
Feb
15
comment How to mathematically determine the number of odd numbers between two integers?
$N_{\text{odd}}(x)=\lfloor (x+1)/2\rfloor$, where $\lfloor\cdot\rfloor$ is the floor function.
Feb
12
revised Solving a delay differential equation
added 136 characters in body; edited tags
Feb
12
revised Solving a delay differential equation
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Feb
12
revised Solving a delay differential equation
deleted 3 characters in body
Feb
12
revised Solving a delay differential equation
added 3 characters in body