39 



from Equation [107]. Therefore Equation [106] holds for all n > s 

 (2) ,1 



I pS pS + \ 



[108] 



We make the substitution, using Equation [06] 

 and Equation [108] becomes 



by Equations [106] and [104] 

 (3) -1 



r ps + lpsAt. 

 ^ -1 VI - K 



c?u (71+ s)! 

 - = 2 



2 (n - s)! 



[109] 



This is proved, by substituting for Vi - fi^ P^, using [97] and integrating, using formulas [104] 

 and [106]. 



(4) 



r , .-1 <^^ (n + s - 1) 

 I p^ ps-i ^ — 2 L 



•'-I Vl -/i in- s + 1)! 



[110] 



Substitute for ^1 - ^^ f„ ^ using Equation [97], and integrate, using [104] and [106]. 

 (5) 



ps pS~l ■ = 



Substitute for J \ - y^ P^ , using [98], and integrate, using [106] and [104]. 

 (6) ri udi 



/•I fJ-d fi 2 (n + s)! 

 psps+l ■ = 



J _i " " y/l-fj? 2n + 1 (n~s~ 



[111] 



[112] 



D! 



Substitute for iiP^ , using [98], and integrate, using [102] and [111]. 



INTEGRAL IN F^^ 



This integral which appears in [29a], is the following 



