
paraspara gaama function

ganithashaasthrathil, reciprocal gaama function aanu function
evideyaanu gaama functione soochippikkunnathu. sankeernamaaya thalatthil ellaayidathum gamma function meromorphic aayathinal poojyamallaathathinaal, athinte reciprocal oru muzhuvan functionaanu. oru muzhuvan pravartthanamenna nilayil, ithu kramam 1 aanu (athaayath athinekkaal vegathil valarunnilla), ennaal ananthamaaya tharatthilaanu (athaayath athinte valarcha idathu-pakuthi thalathinu ekadesham aanupaathikamaayathinaal athinte eathenkilum gunithathekkaal vegathil valarunnu).
gamma functionte samkhyaa kanakkukoottalinulla oru prarambha pooyintaayi reciprocal chilappol upayogikkunnu, koodaathe chila software librarikal ithu saadhaarana gamma functionil ninnu vevvere nalkunnu.
kaal warestrass reciprocal gaama functione "factoriyel" ennu vilikkukayum warestrass factorisation sidhaanthathinte vikasanathil ithu upayogikkukayum cheythu.
ananthamaaya uthppanna vipuleekaranam.
yathaakramam euler, warestrass enniva kaaranam gaama functionte ananthamaaya uthppanna nirvachanagalil ninnu pinthudarnnu, reciprocal gaama functionaayi inipparayunna ananthamaaya uthppanna vipuleekaranam namukk labikkum
euler-masheroni sthiraangam evideyaanu? eee vipuleekaranangal ellah sankeernna samkhyakalkkum saadhuthayullathaanu.
tailor seerees.
0 nuu chuttumulla tailor seerees vipuleekaranam nalkunnu
euler-masheroni sthiraangam evideyaanu? kaaranam, eee padatthinte gunakam aavarthichu kanakkakkaam
riman seetta function evideyaanu? eee gunakangalude oru avibhaajya praathinidhyam aduthide fekih-ahamed (2014) kandethithi
cheria moolyangalkku, iva inipparayunna moolyangal nalkunnu
fekih-ahamed (2014) formula _ 6-nuu oru ekadesha kanakk nalkunnu
ivide soothravaakyam _ 8 umm soothravaakyam _ 9 umm lambert dablyu functionte mainus-phastt shaakhayaanu.
chuttumulla tailor vipuleekaranathinu athe (ennaal marria) gunakangalundu, i.iii.:
(gassinte paii-functionte parasparabandham).
asymptotic vipuleekaranam.
ananthathayilekku pookunnathupoole oru sthiraankathil namukk undu
kondoor integral praathinidhyam.
herman hankel kaaranam oru avibhaajya praathinidhyam
hankel kondoor evideyaanu, athaayath, positteev riyal aaksisiloode muricha branchumaayi bandhappett positteev ananthathayilekku madangukayum positteev dishayil 0-neey valayam cheiyunna paatha. schmelser & trephethan parayunnathanusarichu, haankalinte integralinte samkhyaa moolyanirnayamaanu gaama function anakkukoottunnathinulla chila mikacha reethikalude adisthaanam.
positteev poornnasamkhyakalile avibhaajya praathinidhyam.
positteev poornnasamkhyakalude formula _ 13 nuu, nalkiyirikkunna reciprocal factorial functionu oru integral undu 
athupole, eathu yadhaartha formulakkum formulakkum namukk adutha integral undu yadhaartha akshatthil reciprocal gamma function roopathil 
formula _ 18 reciprocal double factorial functionu vendi oru anubandha bandham nalkumbol, formula _ 19
yadhaartha akshatthil avibhaajyaghadakam.
positteev riyal aaksisiloode reciprocal gaama functionte samyojanam moolyam nalkunnu.
ithu fransen-robinson sthiraangam ennariyappedunnu.
namukk inipparayunna soothravaakyam undu (adhyayam 9, vyayaamam 100)

