
barnes integral

ganit mein, ack barnes integral yaa melin-barnes integral ack samocch integral haye jisamen gaama karyon kaa ack utpaad shamil haye. unake dwara pesh kiya gayaa thaa. way saamaanyikrit atee-jyaamitiya shrinkhala seey nikatata seey sambandhit hain.
samakalan koo aamtaur parr ack samocch key saath liya jaataa haye joe γ ("a" + "s") key roop key sabhi dhruvon key daaeen or aur γ ("a" − "s") key roop key sabhi dhruvon key baain or jaane vaale kaalpanik aksh kaa viroopan haye.
atee-jyaamitiya shrinkhala.
atibhautikiya falan koo ack barnes integral key roop mein diyaa jaataa haye 
bhee dekhein. iss samaantaa koo "s" = 0,1,2, parr avasheshon koo uthaate samay samocch koo daaeen or leey jaakar praapt kiya jaa sakata haye... . sootra _ 2 key liye, aur kaheen aur vishleshanatmak nirantarta dwara. uchit abhisaran sthitiyon koo dekhate hue, koee bhee adhik samanya baarn 'integral aur saamaanyikrit hypergeometric karyon' pee 'aff' kyu 'koo isi tarah seey sambandhit curr sakata haye.
barnes lemma.
pahale barnes lemma raajyon
yeh goss key 2 "f" 1 yog sootra kaa ack anuroop haye, aur euler key beeta integral kaa ack vistaar bhee haye. isamen samakalan koo kabhi-kabhi barnes kaa beeta samakalan kahaa jaataa haye. 
doosara barnes lemma raajyon
jahan "e" = "a" + "b" + "c" − "d" + 1. yeh salschutz key yog sootra kaa ack anuroop haye.
q-barnes integral.
buniyaadi atee-jyaamitiya shrinkhala key liye baarn integral key anuroop hain, aur kaee anya parinamon koo bhee iss mamle mein badhaaya jaa sakata haye.