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May
2
revised Prove $\sum\limits_{n=1}^\infty \frac{n!}{3^n\cdot7\times10\times\cdots\times (3n+1)}=\frac{\pi\sqrt3}{2}+\frac32\ln(3)−4$
added 123 characters in body; edited tags; edited title
May
2
comment Calculation of Integral of $ \int \sqrt{\sec 2x-1}\;dx$ and $ \int \sqrt{\sec 2x+1}\;dx$
Because sometimes, the CAS returns elliptic integral expressions that are correct, but not very useful.
May
2
revised Derivatives of the Struve functions $H_\nu(x)$, $L_\nu(x)$ and other related functions w.r.t. their index $\nu$
added 18 characters in body
May
2
revised What is $f_\alpha(x) = \sum\limits_{n\in \mathbb{N}} \frac{n^\alpha}{n!}x^n$?
added 9 characters in body; edited title
May
2
revised On the inequality $ \int_{-\infty}^{+\infty}\frac{(p'(x))^2}{(p'(x))^2+(p(x))^2}\,dx \le n^{3/2}\pi.$
edited body; edited title
May
2
comment Why are there four independent solutions of Mathieu equation instead of two?
With the Bessels, there is a similar situation to that described by @mickep; you have the two kinds $J_\nu(z)$ and $Y_\nu(z)$, and then you have the Hankel functions which are complex combinations of the two Bessels.
May
2
comment Why does the midpoint method have error $O(h^2)$
You might want to look at the discussion by Hairer/Nørsett/Wanner.
May
2
revised A special modular function: $ j $-invariant.
edited tags
May
2
comment Comprehensive compilation of conic section formulae
@MvG, if memory serves, what I obtained the last time I looked into this was just as horrendous; thanks, nevertheless.
May
2
comment How to reconstruct a symmetric matrix given the eigenvalues and eigenvectors.
Normalize the eigenvectors so that they're mutually orthogonal, and assemble them in a matrix $\mathbf V$. Then with the diagonal matrix of eigenvalues $\Lambda$, form $\mathbf V\Lambda\mathbf V^\top$. I omitted a few details that you should fill in.
May
1
revised Complete Elliptic Integral of the 3rd Kind - Residual Computation
edited tags
May
1
revised transformation involving elliptic integrals
edited tags
May
1
revised Value of an elliptic integral of the first kind
edited tags
May
1
revised How to evaluate the length of the perimeter of a low eccentricity ellipse?
edited tags
May
1
revised Construct a function (curve) that is symmetric about a parabola
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May
1
revised Proof of identity with Hermite polynomials
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May
1
revised Proving a property of Fractional Linear Transformations
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May
1
revised Thinking Problem Involving Average Rate of Change
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May
1
revised Closed form expression for 3F2 with positive unit argument
edited tags
May
1
comment Usage of integration representation
"In numerical calculation?" - sometimes, yes. As an example, one of the integral representations for the Bessel function of the first kind lends itself to a very useful method for numerical evaluation using the trapezoidal rule.