Question

以2π为周期的函数在(-π，π]上的表达式为f(x)=3x2+1，将其展开成傅里叶级数．

Answer 1

【答案】： style='color: rgb(51, 51, 51); text-transform: none; text-indent: 0px; letter-spacing: normal; font-family: arial, helvetica,sans-serif; font-size: 16px; font-style: normal; font-weight: normal; word-spacing: 0px; float: none; display: inline !important; white-space: normal; orphans: 2; widows: 2; background-color: rgb(255, 255, 238); font-variant-ligatures: normal; font-variant-caps: normal; -webkit-text-stroke-width: 0px;'>f(x)在x=π处的左极限为0,右极限为-π,其傅里叶级数在x=π处收敛于左右极限的平均值,即-π/2. style='font-family: arial, helvetica,sans-serif; font-size: 16px;'> x∈(-∞，+∞)