
barnes samagram

ganita saastramlo, barnes integral ledhaa mellin-barnes integral anedi gaama functionla yokka utpattini kaligi unna kantur integral. vaaru parichayam cheyabaddaaru. avi saadhaaraneekarinchina hypergiometric shrenitho daggari sambandham kaligi untaayi.
samagrata saadhaaranamgaa oka aakruti venta teesukobadutundi, idhi γ ("a" + "s") roopam yokka anni kaarakaala dhruwala kudi vaipuku mariyu γ ("a" − "s") roopam yokka anni kaarakaala dhruwala edama vaipuku vellae oohaatmaka aksham yokka vaikalyam.
hypergiometric syries.
hypergiometric function barnes integral gaa ivvabadutundi 
kooda chudandi. s" = 0,1,2, vadda avasheshaalanu teesetappudu aakrutini kudivaipuku taralinchadam dwara eee samaanatvaanni pondavacchu... . suutram _ 2 kosam, mariyu itara chotla vislaeshanhaatmaka konasagimpu dwara. saraina kalayika paristhitulanu batti, marinta saadhaarana barnla integrals mariyu saadhaaraneekarinchina hypergiometric functionlu "p" f "q" nuu idhe vidhamgaa anusandhaaninchavacchu.
barness lemmas.
modati barness lemma rashtraalu
idhi gaas yokka 2 "f" 1 sankalanam suutram yokka saaruupyata, mariyu euler yokka beata integral yokka podigimpu kooda. daanilooni samagratanu konnisaarlu barnes beata samagrata anie pilustaaru. 
rendava barness lemma rashtraalu
ikkada "e" = "a" + "b" + "c" − "d" + 1. idhi salshutz yokka sankalanam suutraaniki saaruupyata.
q-barnes integrals.
praathamika hypergiometric shreniki barnes integrals yokka saaruupyatalu unnaayi, mariyu aneka itara phalitaalanu kooda eee kesuku vistarinchavacchu.

