A Proof that Euler's Constant Gamma is an Irrational Number

On irrational values of the error function and gamma function

In this paper, we establish the irrationality of some open problems in mathematics based on using a recursive formula that generate the complete sequence of numbers. see [1] But before getting into that we begin with some Ramanujan notable work of infinite series and continued fraction.

关于欧拉常数的无理性及相关渐近公式

On irrationality of Euler's constant and related asymptotic formulas

本文利用Sondow的积分表示，推导出相关序列的渐近公式，并借助欧拉常数无理性判据的充分条件，证明了欧拉常数γ是无理数。

$e$ 的无理性的一种新证明

A new proof of the irrationality of $e$

本文给出欧拉数 $e$ 无理性的一个简洁新证明，避免使用连分数和泰勒级数的经典方法。

Two arguments that the nontrivial zeros of the Riemann zeta function are irrational

We have used the first 2600 nontrivial zeros gamma_l of the Riemann zeta function calculated with 1000 digits accuracy and developed them into the continued fractions. We calculated the geometrical means of the denominators of these continued fractions and for all cases we get values close to the Khinchin's constant, what suggests that gamma_l are irrational. Next we have calculated the n-th square roots of the denominators q_n of the convergents of the continued fractions obtaining values close to the Khinchin-Levy constant, again supporting the common believe that gamma_l are irrational.

6阶正则欧拉幻矩阵

A proper Euler magic matrix of order 6

本文针对未被前人解决的6阶正则欧拉幻矩阵问题，给出了γ=18500和γ=43290的两个构造，并确定其计数下界为γ≥2485。

欧拉-马歇罗尼常数的一族新公式

A Family of New Formulas for the Euler-Mascheroni Constant

本研究通过引入E-调和函数，推导证明了欧拉-马歇罗尼常数的两个新公式及一族公式，开展了该函数相关结论的初步探索，为该常数无理性的证明或证伪提供了新的研究基础。