New posts in closed-form

Could this conjecture be proved ? (sum of even powers of cotangents in arithmetic progression )

trigonometry polynomials summation closed-form

Generalized Logarithmic Integral - reference request

calculus integration reference-request logarithms closed-form

Closed form for integral of inverse hyperbolic function in terms of ${_4F_3}$

integration definite-integrals closed-form hypergeometric-function

Does there exist a closed form for $L_k$ for any $k>3$?

sequences-and-series closed-form harmonic-numbers

General integral $\int_0^{\frac{\pi}{p}}\ln\tan x \,dx $

inequality definite-integrals special-functions closed-form

explicit formula for recurrence relation $a_{n+1}=2a_n+\frac{1}{a_n}$

sequences-and-series closed-form

How to find the value of $I_1=\int_0^\infty\frac{\sqrt{x}\arctan{x}\log^2({1+x^2})}{1+x^2}dx$

calculus integration definite-integrals improper-integrals closed-form

Integral $\int^{\frac{\pi}{6}}_{0}\ln^2(2\sin \theta)d\theta$

integration closed-form

How to prove $\int_1^\infty\frac{K(x)^2}x dx=\frac{i\,\pi^3}8$?

complex-analysis definite-integrals special-functions closed-form elliptic-integrals

Closed-Form solution for nested integrals of this polynomial?

calculus integration definite-integrals recurrence-relations closed-form

Derivative of a generalized hypergeometric function

calculus derivatives special-functions closed-form hypergeometric-function

Closed expression for sum $\sum_{k=1}^{\infty} (-1)^{k+1}\frac{\left\lfloor \sqrt{k}\right\rfloor}{k}$

sequences-and-series closed-form ceiling-and-floor-functions

Closed form for ${\large\int}_0^\infty\frac{\arctan(x)\,\operatorname{arccot}(x+1)}{x}dx$

calculus integration definite-integrals closed-form trigonometry

Find $\int\limits^{\infty}_{0}\frac{1}{(x^8+5x^6+14x^4+5x^2+1)^4}dx$

calculus integration definite-integrals closed-form

Request for help to find a closed-form expression for $\sum_{n=0}^{\infty}\frac{(2n+15)^2}{(2n+11)^3\sqrt{(2n+13)}}$

sequences-and-series closed-form

Closed form for ${\large\int}_0^\pi\frac{x\,\cos\frac x3}{\sqrt[3]{\sin x}}dx$

calculus integration trigonometry definite-integrals closed-form

Closed form of $\sum\limits_{i=1}^n k^{1/i}$ or asymptotic equivalent when $n\to\infty$

sequences-and-series asymptotics summation closed-form

Evaluation and generalisation of $\int_0^\infty\int_0^\infty\sin y\frac{\operatorname{gd}(xy)}{\cosh(xy)}\mathrm dx\mathrm dy=\frac{\pi^3}{16}$

integration trigonometry improper-integrals closed-form multiple-integral

Prove that $_4F_3\left(\frac13,\frac13,\frac23,\frac23;1,\frac43,\frac43;1\right)=\frac{\Gamma \left(\frac13\right)^6}{36 \pi ^2}$

sequences-and-series closed-form gamma-function hypergeometric-function elliptic-integrals

How to find closed-form of $\int_{0}^{+\infty} \operatorname{sech}^2 (x^2)\,dx$

calculus integration definite-integrals improper-integrals closed-form