Entwickchmgen zum J^a (jr an ge' sehen IxcversioDslhcoynn, etc. 135 



=pD'-^ [(p-l)(p-2)ij^-5)f"-^r+ g)(j,_l)Q;_2)i.v-3.^'^+ g)Q>-])i^-^)/-'+^V ' ] 



also allgemein: 



+ (|) (/'-!) • • {p-q + ?>)F\r''+'''f"' '+ (|)(J'- 1) • ..{p^q+A)FiP-':+^-^f:-^+ . . . 



+ ... (^^Yp—]) . . .(p^q + ni)F[i;-'>^'"-') /■''i-"'+ ... j 4) 

 wcim uiau abkiirzimgsweise setzt: 

 i^W =/•'•/■" 

 F^)z=if'-f"' ' 



j'^i'-.' =/■'•/■• +io/,'/'''-'/-7"' 



Ff^f'-r' + bl-p-' {3f"r+2f"'^)+lbk{k—l)f'^-^f"'^ 



Ff = ['■/■'" +7kf-\3f"f +bf"'f")+10bk{k-l)p-YY' 



F(/> = Pf "'+Uf''- ' {Af"f' + %f"'f+br^) + 10h (I.— Df" ' (3f"^f"+4:f"f"'^) + 



+ 10bk (/.■- 1 ) {k-2)f'-''f'\ 

 F«=/'7''-^ + G/.:f-'((3/'7'*''+14/-"7''+21/'7M + 14Ä:a" ---!)/•'■- 



+ 1 2mk{k- 1) (/.: - 2)f - Y"7 

 i'W — /• Y^ + 3Ä- /■'•-' ( lö/'"/-'- '" + ■J (y'" /■'■" + 70/'" / " + A2f 2) H- ] OöA- i^Ä-— 1 •) /•'-= ((:;/■"«/■" + 24f"f"'f + 



+ 1 5^vyv, 2_^ 20/'" Y" ) + 31 r)OÄ;(/c- 1 )( A'- 2) f'^-\fi^p + 2/"V"'2j + 945/>( /,■- 1)(A - 2 )(k—3)f -"/"■■ 

 /'/• ' = /''7'"+ 1 1 /.■/•-' (5/'"/'" + 1 bf'"f' '" + 30/''7"'+ 42/' /■' ') + 165Ä^ [k- 1) /''-= (ßf'^f " + 28f"f"'p ' + 

 + 42/'7'" /■' + 28/'"'7' + 35 /■"7" 2 ) + 770/,- ( /,•— 1) ( A-- 2 )/'-3 O/''^'^ +4bfY"f" + 20f"f'"^) + 



+ 17325/i-(A:— 1)(A-— 2)(A'-3)f'-V"7'"' 



Zwischen diesen /'-Functionen besteht folgende, einfache Relation, nach welcher man sie successive sehr 

 bequem berechnen kann: 



Ff = DFij;) -kf'Fi^-')+3kf"F(['-') ■, 



Ff)—DF^) -kf'F<-^-')+4kf"F(^-*) I 



F'!-'' = D Fi''' —kf'Ff-^^ + bkf" F^''~'> C !'■* 



Lässt man in der Gleichung 4) g = /- undj;=:« + l sein, so wird: 



D'f"+'z=(n+l)H{n~l)...(n-r+2)f"-- + 'f''-h ('^) (m+1). . . (H-r + 3j i'"^"-"+2)f '-= + 



+ (!;)(// + 1).. .{H-r + 4) F}^'-'+'^>f''-~^ + . . . (^''Yn + l) . ..{H-r+m+l) F'-'^-'+'-'P' 



