98 



a H- 111 —/\ /'n \ n 



' siiivaiit 



"1 — 2A / \ Z / ;j (n — /)! 



Ol iiilrodiiisoiis la iicUalioii Eiilcricnnc soit ii! = r (ii -(- 1). 

 Noiis aiii'ons: 



,,-^,^^,_ V (— 1) • r(m — ;> + !) r (a -f m — ;. + 1) / 2 V" - -^- 

 -^ ' ,^ r(/i + 1) r(in — 2 A + 1) r(a -|- a -t^i) V x J 



011 rnnsiflöranl lim ni ■.= co, nous aiiroiis 



P " .0 _'^ ( - 1)' -r-jm - Z + 1) 7- (a --1- 111 - A + 1) /_2^Y"-2;. 



^ IV H- 1) a"i ~ 2 /i -I- 1) r(a + z f 1) U ; 



Rappolons eiicoro quo 



r(n 4- a) =n" Tu *) 

 poiir lim n =^ c>o. 

 Nous aiiroiis alors: 

 r(m -f 1— 2Z) = r((m + 1 — X) — X) = {m - l^-l)-^ r{m~l-}-l) 

 r((m-A+l)-|-a) = (m - l -]- if r(m — >^ -f- 1). 



a 



Ell iiUrodiiisaiil cos valeiirs daiis la fonclioii P„j(\). nous olUcnons: 

 pa , J'x^ C - 1)^ r(ni-A+ l) (m-vl+lf r(m-H-l) /^\m~^' 



A-0 



On aiira de rnöme 



- ^ -I- 1) 



= r(iii + a + 1) = (111 |- a)! 



(111 - / I- 1)'" ^- r(iii — l -\- 1) = r(m — / + 1 + A I- a) 



1 



On poiil romi)lacer - par 



2-^'rM + 4 



^! r(i)(2;,)! 



CO (pii doiuio: 



*) Prof. Dr. J. II. Graf. Ki ii loi I ii ii li- in dir Tliooric di-r (iaminn- 

 funktion, pagc 5. Born, 1894. 



