Newbetuts

What is the role of mathematical intuition and common sense in questions of irrationality or transcendence of values of special functions?

$\int_0^1\arctan\,_4F_3\left(\frac{1}{5},\frac{2}{5},\frac{3}{5},\frac{4}{5};\frac{1}{2},\frac{3}{4},\frac{5}{4};\frac{x}{64}\right)\,\mathrm dx$

a conjectured continued fraction for $\tan\left(\frac{z\pi}{4z+2n}\right)$

Why is the error function defined as it is?

Why isn't the gamma function defined so that $\Gamma(n) = n! $?

An integral involving Fresnel integrals $\int_0^\infty \left(\left(2\ S(x)-1\right)^2+\left(2\ C(x)-1\right)^2\right)^2 x\ \mathrm dx,$

Non-trivial values of error function $\operatorname{erf}(x)$?

Extending the result $\int_{0}^{\infty} \left( ( 1 - 2C(x))^{2} + (1-2S(x))^{2} \right) \, dx = \frac{4}{\pi} $

Definite Dilogarithm integral $\int^1_0 \frac{\operatorname{Li}_2^2(x)}{x}\, dx $

Why can't we define more elementary functions?

How to evaluate $\int_0^\infty\operatorname{erfc}^n x\ \mathrm dx$?

What does | mean?

The special case of Pochhammer Symbol at Zero?

Proof of dilogarithm reflection formula $\zeta(2)-\log(x)\log(1-x)=\operatorname{Li}_2(x)+\operatorname{Li}_2(1-x)$

Evaluating $\int_0^\infty \frac{dx}{1+x^4}$. [duplicate]

Is there a function whose antiderivative can be found but whose derivative cannot?

A Challenging Logarithmic Integral $\int_0^1 \frac{\log(x)\log(1-x)\log^2(1+x)}{x}dx$

New posts in special-functions

What is the role of mathematical intuition and common sense in questions of irrationality or transcendence of values of special functions?

Easy explanation of analytic continuation

Other interesting consequences of $d=163$?

Evaluating the series $\sum\limits_{n=1}^{\infty} \frac{1}{n^{3} \binom{2n}{n}} $

$\int_0^1\arctan\,_4F_3\left(\frac{1}{5},\frac{2}{5},\frac{3}{5},\frac{4}{5};\frac{1}{2},\frac{3}{4},\frac{5}{4};\frac{x}{64}\right)\,\mathrm dx$

a conjectured continued fraction for $\tan\left(\frac{z\pi}{4z+2n}\right)$

Why is the error function defined as it is?

Why isn't the gamma function defined so that $\Gamma(n) = n! $?

An integral involving Fresnel integrals $\int_0^\infty \left(\left(2\ S(x)-1\right)^2+\left(2\ C(x)-1\right)^2\right)^2 x\ \mathrm dx,$

Non-trivial values of error function $\operatorname{erf}(x)$?

Extending the result $\int_{0}^{\infty} \left( ( 1 - 2C(x))^{2} + (1-2S(x))^{2} \right) \, dx = \frac{4}{\pi} $

Definite Dilogarithm integral $\int^1_0 \frac{\operatorname{Li}_2^2(x)}{x}\, dx $

Why can't we define more elementary functions?

How to evaluate $\int_0^\infty\operatorname{erfc}^n x\ \mathrm dx$?

What does | mean?

The special case of Pochhammer Symbol at Zero?

Proof of dilogarithm reflection formula $\zeta(2)-\log(x)\log(1-x)=\operatorname{Li}_2(x)+\operatorname{Li}_2(1-x)$

Evaluating $\int_0^\infty \frac{dx}{1+x^4}$. [duplicate]

Is there a function whose antiderivative can be found but whose derivative cannot?

A Challenging Logarithmic Integral $\int_0^1 \frac{\log(x)\log(1-x)\log^2(1+x)}{x}dx$