Search results for "Bernoullin luvut"

showing 2 items of 2 documents

Bernoullin luvut ja Euler-MacLaurinin summakaava

2007

Bernoullin luvutEulerin summakaavaBernoullin polynomitEuler-MacLaurinin summakaava

Eulerin summia

2014

Tämän tutkielman tarkoituksena on tarkastella menetelmiä joilla voidaan laskea niin kutsuttuja Eulerin summia. Eulerin summia ovat Riemannin zeeta-funktion arvoja parillisissa ja positiivisissa kokonaislukupisteissä. Vaikka kyseessä on ääretön joukko äärettömiä summia, niin Eulerin summien laskemiseksi on mahdollista johtaa eksplisiittinen kaava. Tämä kaava johdetaan tutkielmassa kahdella eri tavalla: Bernoullin lukuja ja toisaalta Fourier-analyysin tuloksia hyödyntäen. Lisäksi tutkielmassa tarkastellaan muutamia menetelmiä, joilla voidaan laskea yksittäisiä Eulerin summia. Huomionarvoinen maininta on, että vaikka mielivaltainen äärellinen Eulerin osasumma on rationaalinen, niin kaikki Eule…

sarjateoriaRiemannin zeeta-funktioBernoullin luvutFourier-sarjatfunktiot

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