Search results for "Bernoullin polynomit"

showing 2 items of 2 documents

Bernoullin luvut ja Euler-MacLaurinin summakaava

2007

Bernoullin luvutEulerin summakaavaBernoullin polynomitEuler-MacLaurinin summakaava

Reaalianalyyttistä lukuteoriaa

2016

Tämän tutkielman tarkoituksena on tutustuttaa lukija Bernoullin polynomeihin, Γ-funktioon ja lukuteoreettisiin Mertensin lauseisiin. Näiden lisäksi tutkitaan erästä lukuteoreettista tuloa, ja esitellään tähän tuloon liittyviä tiettävästi uusia tuloksia. Bernoullin polynomien avulla todistetaan erityisesti Euler-Maclaurinin lause, joka kertoo erilaisten summien ja integraalien välisestä yhteydestä. Γ-funktion avulla taas todistetaan Stirlingin kaava, joka antaa hyvän approksimaation kertoman n! kasvu- nopeudesta. Mertensin lauseista ensimmäinen kertoo, miten nopeasti lukua n pie- nempien alkulukujen käänteislukujen 1/p summa hajaantuu, kun kasvatetaan lukua n. Toinen Mertensin lause kertoo, …

lukuteoriaphi-torialalkuluvutBernoulliGammaMertensin lauseBernoullin polynomitGamma-funktioMertens

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