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anuttarasammyak's latest activity
anuttarasammyak
replied to the thread
POTW
Sum of an Alternating Series
.
Excellent. Let me follow you. T(x):=\sum_{n=1}^{\infty}\frac{\sin(n(\pi-x))}{n^3} for ##-\pi < x < \pi##. Regarding this as Fourier...
Yesterday, 8:44 PM
anuttarasammyak
reacted to
renormalize's post
in the thread
I
Eigenstates of particle with 1/2 spin (qbit)
with
Like
.
Did you mean to write ##|\psi\rangle=\alpha\cos(\theta/2)|\uparrow\rangle+\beta e^{i\varphi}\sin(\theta/2)|\downarrow\rangle##?
Yesterday, 6:37 PM
anuttarasammyak
reacted to
Svein's post
in the thread
POTW
Sum of an Alternating Series
with
Like
.
As I have noted in an Insight, just create the Fourier serien from the function \pi ^{2}\cdot x - x^{3} . This ends up in 12\cdot...
Thursday, 8:56 AM
anuttarasammyak
reacted to
julian's post
in the thread
POTW
Sum of an Alternating Series
with
Like
.
Wednesday, 1:54 AM
anuttarasammyak
replied to the thread
POTW
Sum of an Alternating Series
.
I would try another transformation S=Re(-i\sum_{n=1}^\infty \frac{e^{\frac{\pi n i}{2}}}{n^3}) =\lim_{x\rightarrow 1} Re(-i (\frac{\pi...
Tuesday, 8:42 AM
anuttarasammyak
reacted to
Max123's post
in the thread
Why don't hydrogen ions have osmotic activity in living organisms?
with
Like
.
Well, my professor said thst H3O+ behaves exactly like water and doesnt increase osmolality
Monday, 7:03 AM
anuttarasammyak
replied to the thread
Why don't hydrogen ions have osmotic activity in living organisms?
.
Then have you known osmotic behaviour of H3O+ ion, which could cease your question ?
Monday, 2:40 AM
anuttarasammyak
replied to the thread
Why don't hydrogen ions have osmotic activity in living organisms?
.
So your question seems why only neutral atoms and molecules pass the membrane ? I say it in logic. I do not know the facts.
Sunday, 7:20 AM
anuttarasammyak
replied to the thread
Why don't hydrogen ions have osmotic activity in living organisms?
.
Do you mean any postive charged ions cannot pass membrane or hydrogen ion only ?
Sunday, 7:13 AM
anuttarasammyak
replied to the thread
Why don't hydrogen ions have osmotic activity in living organisms?
.
Though I am not good at chemistry, I think hydrogen ion, i.e. proton and proton-neutron core, pass the semipermeable membrane including...
Sunday, 7:01 AM
anuttarasammyak
replied to the thread
Particle confined in 3D box - quantum states
.
In a narrow sense of mathematics, you are right. But in physics almost all the numbers in calculation is approximate. I am afraid...
May 3, 2024
anuttarasammyak
replied to the thread
Particle confined in 3D box - quantum states
.
I asked Wolfram as shown There seems no integers to satisfy the relation. In neighbor, (2,3,27) satisfies a^2+b^2+c^2=582 and...
May 2, 2024
anuttarasammyak
replied to the thread
POTW
Sum of an Alternating Series
.
Thanks for pointing out the difficulty. From my last line \frac{8}{\pi^3}S=\frac{1}{2}\int_{0}^{\infty} p^2 dp \ (\sum_{n=1}^\infty...
May 1, 2024
anuttarasammyak
replied to the thread
Solve the equation : ##x^4+12x^3+2x^2+25=0##
.
I am afraid that in this way we would not succed to reduce the effort than solving the equation itself.
May 1, 2024
anuttarasammyak
replied to the thread
POTW
Sum of an Alternating Series
.
Inspired by answer of julian, let me show my sketch using Fourier transform and distribution.
Apr 30, 2024
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