Title: Fourier Analysis and the closed form for the Zeta Function at even positive integers Show Chinese title

Title: 傅里叶分析和黎曼ζ函数在正偶数处的闭合形式

Abstract: Using a summation identity obtained for the Fourier coefficients of $x^{2k}$, we derive a closed form expression for the zeta function at even positive integers, using a technique similar to one in an existing proof by Aladdi and Defant[1], but in a simpler and shorter way. Show Chinese abstract

Abstract: 使用针对$x^{2k}$的傅里叶系数得到的求和恒等式，我们推导出在正偶数处的zeta函数的闭合表达式，采用类似于 Aladdi 和 Defant[1] 现有证明中的技术，但以更简单和简短的方式。