Re: [分析] 複變證明
※ 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)
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04/03 11:26, , 1F
04/03 11:26, 1F
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