Re: [分析] 複變證明

[womack79 (糖做的老虎)]

※ 引述《gauss760220 (章魚)》之銘言：
: sin(iz)=i*sinh(z)
: sinh(iz)=i*sin(z)
: 請問有人知道這式子該如何證明嗎?
: 看了一下還是不太懂@@"

sin(z) = (1/2i)[e^(iz) - e^(-iz)]

=> sin(iz) = (1/2i)[e^(-z) - e^z]

           = (i/2)[e^z - e^(-z)]

           = isinh(z)

sinh(z) = (1/2)[e^z - e^(-z)]

=> sinh(iz) = (1/2)[e^(iz) - e^(-iz)]

            = i(1/2i)[e^(iz) - e^(-iz)]

            = isin(z)

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 140.113.68.127
→ gauss760220 :謝謝^^