推 johncai :果然要用到高等數學@@~~~感謝!!! 12/05 17:43
※ 引述《johncai (@@)》之銘言：
: Y=((1-e^(-AD))/AD)^2
: 已知Y及A..求D
: 謝謝...
令 x = AD, k = √Y
1-e^-x
原式成為 -------- = k
x
可化為 e^-x = -kx + 1 = -k(x - 1/k)
其解以 Lambert W function (aka. ProductLog) 表示為
1 -1
x = --- + W(----------)
k ke^(1/k)
(見以下連結的公式:
http://en.wikipedia.org/wiki/Lambert_W_function#Generalizations
公式中 c = 1, a0 = -k, r = 1/k)
因為以 W 函數表示的關係它不能以初等函數表示
所以你就拿個數學軟體去跑好了
大多數有支援的軟體都能用 LambertW (可能小寫) 叫出這個函數
--
'Oh, Harry, don't you see?' Hermione breathed. 'If she could have done
one thing to make absolutely sure that every single person in this school
will read your interview, it was banning it!'
---'Harry Potter and the order of the phoenix', P513
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 210.69.49.38