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Just an adult math student, trying to learn a few interesting things while passing through this world.


1h
comment Bessel Functions Proof
Use the identity here: en.m.wikipedia.org/wiki/Jacobi%E2%80%93Anger_expansion for $\sin(z\cos\theta)$, and apply the orthogonality of cosines of the form $\cos(n\theta), \cos([2n-1]\theta)$ on the interval $[0, \frac{\pi}{2}] $.
Apr
4
comment integral involving incomplete gamma function
I think integration by parts should work, using the definition of the derivative of the incomplete gamma function wrt y given on the wikipedia page.
Apr
4
comment Numerical Solution of $\frac{x}{1-e^{-x}} -5 = 0$
The solution can be expressed in terms of the Lambert W function, $x = W(\frac{-5}{e^5}) + 5$
Apr
1
comment Can you solve this Lagrange differential equation?
The equation in red is separable.
Mar
18
comment Is there any quick method to solve this second-order semilinear ODE
The substitution shown transforms the original ODE into an Abel equation of the second kind
Mar
15
comment Function to create a smooth, monotonically non-decreasing curve between three points
Maybe put point A at the point of inflection of $C_1\mathrm{sech}(C_2 x)$, for some constants c1 and c2. Connect A and B with the sech, and then join a parabola from B to C?
Mar
15
comment Function to create a smooth, monotonically non-decreasing curve between three points
Can the function be defined piecewise?
Mar
15
comment Average Length Of Queue
See en.wikipedia.org/Little's_law .
Feb
27
awarded  Yearling
Feb
26
accepted Expressing $\mathrm{B}(\sinh(x), \cosh(x))$ in terms of elementary functions
Feb
24
revised Expressing $\mathrm{B}(\sinh(x), \cosh(x))$ in terms of elementary functions
edited title
Feb
24
comment Expressing $\mathrm{B}(\sinh(x), \cosh(x))$ in terms of elementary functions
In looking at this problem I noted that while $\Gamma(\cosh(x) + \sinh(x)) = \Gamma(e^x) = e^{-x}e^{x!}$ and $\Gamma(\sinh(x)) = {\rm csch}(x)\sinh(x)!$, I could not seem to find an equivalent expression for $\Gamma(\cosh(x))$. Frustrating!
Feb
24
asked Expressing $\mathrm{B}(\sinh(x), \cosh(x))$ in terms of elementary functions
Dec
27
awarded  Notable Question
Dec
4
asked Weierstrass and Borel summation
Dec
1
comment Application of exponential distributions
Hint: Check out the properties of the cumulative distribution function for the exponential distribution. en.wikipedia.org/wiki/…
Nov
29
comment Wave-Particle Duality in PDE?
I hope you get a good answer to your question; I'd just like to thank you for the link to the text. It does look like a good book - and it is short!
Nov
28
comment linear ordinary differential equation
Hi randy, welcome to Math SE. In general, it is considered good practice when asking what seems to be a homework question to include details of what work/methods you have already used in attempting to arrive at a solution. This shows that you have put effort into solving the problem, and allows other users to provide better answers.
Nov
25
revised How can I prove that these integrals do not converge?
Added LaTeX, grammar.
Nov
25
suggested suggested edit on How can I prove that these integrals do not converge?