आयलर संख्याएँ
ayalar sankhyaean ayalar (aauyalar) sankhyaoan ka nam jarman ganitajn liyonard aauyalar ke nam par rakha gaya hai. ye sankhyaean ayalar bahupadoan (p aaulinomiyals) se utpann hoti haian:
yadi
chitr:Euler-1.gif
jahaan ee nepariy laghuganakoan ka adhar hai aur
a0n (y) = yan,
to a0n(y) ko ghat n aur varn (aaurdar) shoony ka ayalar bahupad kahate haian.
varn s ke ayalar bahupadoan ki paribhasha yah hai: chitr:Euler-2.gif y =1/2s rakhane se 2nan() (y) ke jo man prapt hote haian, unhean varn s ki ayalar sankhyaean an() kahate haian. visham pratyay (safiks) ki samast ayalar sankhyaean shoony ho jati haian.
is prakar an (s)=2 an(s) (1/2s).
an (1)(s) ke lie ham an(s) likhate haian. chitr:Euler-3.gif
ham janate haian ki ka punarvinyas karake y2p ke gunaank ko shreni 1/4p vyukae 1/2 py ke pad y2p ke gunaank ke saman rakhane se hamean yah prapt hoga:
chitr:Euler-4.gif
is sanbandh se spasht hai ki ayalar sankhyaean barabar badhati jati haian aur pratyek sankhya ka chinh badalata jata hai, arthath ve kramanusar ghanatmak aur rrinatmak hoti haian.[1]
ka man saranik ke roop mean hota hai. chitr:Euler-5.gif
barnooli sankhyaoan ki bhaanti ayalar sankhyaean bhi saankhyiki staitistiks) mean aantarveshan (iantarapoleshan) mean prayukt hoti haian.[2]
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tika tippani aur sandarbh
sanbandhit lekh