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16h
comment Show that $J_n(x)$ satisfies Bessel equation $ x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx} + (x^2 - n^2)y = 0 $
also math.stackexchange.com/questions/359107/…
16h
asked Show that $J_n(x)$ satisfies Bessel equation $ x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx} + (x^2 - n^2)y = 0 $
1d
answered Representing a linear operator on $V$ with an element of $V \otimes V^*$
Feb
4
accepted How to derive $\sum_{n=0}^\infty 1 = -\frac{1}{2}$ without zeta regularization
Jan
29
accepted Does $\overline{ \sqrt{1 + i}} = \sqrt{1-i} \ $?
Jan
29
comment Does $\overline{ \sqrt{1 + i}} = \sqrt{1-i} \ $?
The paper that I am reading is unusual as they are cutting along $\mathbb{R}^+$ instead of $\mathbb{R}^-$ I should have mentioned that thanks.
Jan
29
comment Does $\overline{ \sqrt{1 + i}} = \sqrt{1-i} \ $?
what if you cut at positive reals?
Jan
29
asked Does $\overline{ \sqrt{1 + i}} = \sqrt{1-i} \ $?
Jan
26
answered If $[x+0.19] +[x+0.20] +[x+0.21] +\cdots [x+0.91] =546$ find the value of $[100x]$..
Jan
26
accepted express as contour integral $ f(x) = \int_0^\infty dt \; e^{-t/g} \; \frac{1}{\sqrt{1 - 2 t x}} $
Jan
26
comment express as contour integral $ f(x) = \int_0^\infty dt \; e^{-t/g} \; \frac{1}{\sqrt{1 - 2 t x}} $
Yeah this could be the one
Jan
25
revised express as contour integral $ f(x) = \int_0^\infty dt \; e^{-t/g} \; \frac{1}{\sqrt{1 - 2 t x}} $
edited body
Jan
25
comment express as contour integral $ f(x) = \int_0^\infty dt \; e^{-t/g} \; \frac{1}{\sqrt{1 - 2 t x}} $
@tired yes. the $e^{\frac{1}{2g}}$ is an instanton correction
Jan
25
comment express as contour integral $ f(x) = \int_0^\infty dt \; e^{-t/g} \; \frac{1}{\sqrt{1 - 2 t x}} $
@tired you get the error function if you don't add any correcting terms wolframalpha.com/input/… that's why I started making stuff up. it comes from a physics paper
Jan
25
asked express as contour integral $ f(x) = \int_0^\infty dt \; e^{-t/g} \; \frac{1}{\sqrt{1 - 2 t x}} $
Jan
24
comment How to prove that $f$ is integrable if $\forall \epsilon, \ \exists$ partition $M\in [a,b]$ such that $U_f(M) - L_f(M)\lt\epsilon$?
In practice these partitions might get pretty exotic. What partition makes the upper and lower Riemann sums close when $f(x)=\sum_{n=0}^{100}\frac{1}{n}\sin nx$ ? This converges to a sawtooth wave
Jan
22
comment How is the B-Spline definition constructed?
Please look at these notes pomax.github.io/bezierinfo I can provide more discussion later
Jan
21
comment Proof verification for $A \subset B$ iff $A - B = \varnothing$
I always found $A-B$ to be a finmy notation for sets since we're showing $A$ is inside $B$. Technically A "subset" of B
Jan
19
asked Show $ \mathbb{F}_2[x]/(x^3 + x^2 + 1) \simeq \mathbb{F}_2[t]/(t^3 + t + 1)$
Jan
19
comment Cartan Lie Algebra of the Unitary Group $U(N)$?
I also found this resource astro.sunysb.edu/steinkirch/books/group.pdf