计算Gamma（x + 1/2）/ Gamma（x）

Question

I need to compute Gamma(x+1/2)/Gamma(x) for reasonably large x. 我需要为相当大的x计算Gamma（x + 1/2）/ Gamma（x）。 If I just use http://docs.scipy.org/doc/scipy/reference/generated/scipy.special.gamma.html it fails as the denominator and numerator are huge. 如果我只使用http://docs.scipy.org/doc/scipy/reference/generation/scipy.special.gamma.html，则它会失败，因为分母和分子很大。 However the fraction itself is around sqrt(x). 但是，分数本身约为sqrt（x）。 How can I compute this fraction accurately? 如何准确计算这个分数？

Answer 1

you can use beta(a, b) = gamma(a) * gamma(b) / gamma(a+b) 您可以使用beta(a, b) = gamma(a) * gamma(b) / gamma(a+b)

from scipy.special import gamma, beta
x = 10
print gamma(x+0.5)/gamma(x)
print gamma(0.5)/beta(x, 0.5)