Some important formulas involving gamma functions 541 5. some important formulas involving gamma functions first we evaluater by definition (5.1) t(4) = át. (note that it does not matter what letter were for the dummy wariable of in tegration in a definite integral.) put t = yin (5.1); then dt = 2ydy, and (5.1) becomes ra)=l*1872, dy=2ſ 3d or, with x as the dummy integration variable, multiply these two integrals for integral: (b) together and write the result as a double [td-- --) de dy this is an integral over the first quadrant; it can be more easily evaluated in polar coordinates [r)-"i c *rdrdo 4 1 5 -- therefore (5.3) (5.3) tv) - vz. we state here another important forma chapter 14, section 7. example 5): involving functions for proof. se (5.4) (p) (1 – p) = notice that (5.4) also gives (t) = vif we put p= }