Some important formulas involving gamma functions 541 5. some important formulas involving gamma functions first we evaluater by definition t(4) = a*at. (note that it does not matter what letter wee for the dummy wariable of in tegration in a definite integral.) put t = yin (5.1); then dt = 2ydy, and (5.1) ra)=l*1*3*2dy=2ſ 3d or, with x as the dummy integration variable, (5.2) multiply these two integrals for integral: (b) together and write the result as a double ***]de dy. this is an integral over the first quadrant; it can be more easily evaluated in polar coordinates: re1)-"i *rdrdo + 5 -- therefore (5.3) (5.3) r) vi. ) = we state here another important formula involving chapter 14, section 7. example 5): functions for proof. se (5.4) (p) (1 – p) = notice that (5.4) also gives () = = if we put p=>