m****e
发帖数: 488 | 1 正在做的一个project需要一个积分，可是推不出closeform，只好求助大家
我化简如下，对x从0到1积分
[x^a*(1-x)^b]/(1-c*x)
a,b,c为参数，其中0
谢谢 | n**m
发帖数: 156 | 2 分成 rx+s+t/(1-c*x)，然后再积分？ | s******h
发帖数: 539 | 3 When a and b are not integers, it is generally hard to factor it into the
form of rx+s+t/(1-c*x).
This is a simple example of a type of famous integrals, see Prudnikov et al.
, 1986, volume 1 for details.
The "closed" form of your integral is
\int_0^1 x^a(1-x)^b/(1 - cx)dx = B(a+1, b+1)2F1(a+1, 1; a+b+2, c), where
2F1(.) is the Gaussian hypergeometric function
http://en.wikipedia.org/wiki/Hypergeometric_function |
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