296 



Leopold Gegenbauer. 



> Lj^ > 2Ml(M-)-2v-] 



y 



2^-'[n(v-i)]V„ 



U +n 



^ l(«/-)-x--(-cosy^^a;*— 1) ^ Ji^([/«/4-a;-t-coS5>|/a;*— 1) gini" ~' yrff> 



17) J^+«^lA2/) = (-2)"y ^- (« + v)II(w) 





(1— a;') ^ C,Xa;Va; |(«/-t-a;-i-cosylAa;^— 1) - /!"(]/ (/H-a;-i-cos j^lAa;*—!) sin ^"-' y(7y 



n(2v-l) 



"(M-f-VJlI(«) 



.+1 



[2-.„(.-.)n{?^)J 





19) Jv{\/f^z) = v(y -t- s) 2 (1 -z^) 



n(2v-l) 



r2v—i\ 



2^"-.n(v-i)n(^^j 





(l—x*) ' dx ( /- - r/" 7^=^ 



j~-^^^^— ^—^jil/ -hx-h cos f]/x^-l) 2j^([/2/_t_a;^co8yl/a;*-l)sin^'-' yrfy 



n =oo 



2"n(ww-2v-l) 



22-'-'[Il(v 



[JL — 71 



21) Ji'-" (l/^) = 2"ij 2~ („-I- v)ll(w) 



Uy-hx-hCOSf^x^—l) ^ J^(\/ y-hx-hcosf'/x'^—l) sin 2"-' yjrfy 



n(2v-i) 



/2v-l 



22v-in(v-i)n(- 2 



(1— a;*)~^^ Cl{x)dx l(y+x-i-cmf^/x^^yjf-{\fy-hx-hCOS^\fx^^^) sin^v-« ^(ij, 



• +" 



2^) Z 



y ^ Jv--'\\l y) z^ _ 

 2"(w-l-v)n(w) ' 



n(2v-l) 



.+1 



2=-'-'n(v-i)n(-^)_ 



2v— 1 />^ 



d-a;') ^ ffa _^ ^ _^ ß(,g /^«^) "^ Ji^flA^ X -H cos y lAa^^^^'sin 2'-' yfl!op 

 (1 — 2^a;-i-2^r' i,, '^ J ^J Ti .. r r 



23) J^{\fy^z). 



■;_, (l-2^a;-i-27';o 



v(i-;2«) r n(2v-i) 



(ly-^z) " 



2^-'n(v-i)ri(^)_ 



I ^^~J^''^ '/"'. (V -H ^-+- cos ylAi«^)"~^ j^(^«^cc-,-cosy/a:«-l) sin^^-' yrfy 



■J_, (1— 22:a;-*-2'')''"^' ; ^ ^ 



