※ 引述《pulist (momo)》之銘言:
: 請問如何從6.16積分得到6.17
: https://i.imgur.com/P3IaAuo.jpg
: https://i.imgur.com/l2R8Bd4.jpg
α = a > 0
|x - ξ| = t > 0
留數定理
I = [a^4 /(2πk)](2πi) *
{exp(itaexp(π/4))/[4exp(i3π/4)a^3] +
exp(itaexp(3π/4))/[4exp(i9π/4)a^3}
= [a/(4k)]exp(-at/√2){exp(ita/√2)(-i)exp(iπ/4)
+ exp(-ita/√2)(i)exp(-iπ/4)}
= [a/(2k)]exp(-at/√2)sin(ta/√2 + π/4)
= [α/(2k)]exp(-|x - ξ|α/√2)sin(|x - ξ|α/√2 + π/4)
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