Which of the following is not the definition of Beta function?
Posted: Thu Jul 14, 2022 9:29 am
a) \(\beta(m, n) = 2\int_0^1 x^{m-1} (1-x)^{n-1} dx (m>0, n>0) \)
b) \(\beta(m, n) = 2\int_0^{π/2}(sinθ)^{2m-1} (cosθ)^{2n-1} dθ \)
c) \(\beta(m, n) = \int_0^∞ \frac{y^{n+1}}{(1+y)^{m+n}} dy \)
d) \(\beta(m, n) = \int_0^1 \frac{x^{m-1}+x^{n-1}}{(1+x)^{m+n}} dx \)
b) \(\beta(m, n) = 2\int_0^{π/2}(sinθ)^{2m-1} (cosθ)^{2n-1} dθ \)
c) \(\beta(m, n) = \int_0^∞ \frac{y^{n+1}}{(1+y)^{m+n}} dy \)
d) \(\beta(m, n) = \int_0^1 \frac{x^{m-1}+x^{n-1}}{(1+x)^{m+n}} dx \)