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 May2 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 May2 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. May2 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 May2 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 May2 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 May2 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. May2 comment Why does the midpoint method have error $O(h^2)$ You might want to look at the discussion by Hairer/Nørsett/Wanner. May2 revised A special modular function: $j$-invariant. edited tags May2 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. May2 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. May1 revised Complete Elliptic Integral of the 3rd Kind - Residual Computation edited tags May1 revised transformation involving elliptic integrals edited tags May1 revised Value of an elliptic integral of the first kind edited tags May1 revised How to evaluate the length of the perimeter of a low eccentricity ellipse? edited tags May1 revised Construct a function (curve) that is symmetric about a parabola edited tags May1 revised Proof of identity with Hermite polynomials edited tags May1 revised Proving a property of Fractional Linear Transformations edited tags May1 revised Thinking Problem Involving Average Rate of Change edited tags May1 revised Closed form expression for 3F2 with positive unit argument edited tags May1 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.