اقتران ريمان الزائي
الدالة زيتا (اِقْتِرانُ ريمان الزَّائِيُّ حسب مجمع اللغة العربية بالقاهرة) دالة خاصّة لها أهمية عظيمة في نظرية الأعداد. تعريفها المشهور الصالح لأجل
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يمكن تعريفها بصيغ أخرى عدبدة نخص بالذكر منها جداء أويلر
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التعريف
صيغة الدالة للأعداد الزوجية
هذه الصيغة تنسب لأويلر، وهي تعطي قيمة ζ(2k) للأعداد الزوجية:
حيث B2k هي أعداد بيرنولي.
و هذه بعض القيم:
ζ(2) = π2/6, ζ(4) = π4/90, ζ(6) = π6/945, ζ(8) = π8/9450
أما بالنسبة للأعداد الفردية, فلا توجد صيغة لحساب زيتا. فقط نعرف قيمة 3 التي هي: ζ(3) = 1,2020569 ،
انظر أيضاً
الهامش
- ^ "Jupyter Notebook Viewer". Nbviewer.ipython.org. Retrieved 2017-01-04.
المراجع
- قالب:Dlmf
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وصلات خارجية
- Hazewinkel, Michiel, ed. (2001), "Zeta-function", Encyclopaedia of Mathematics, Kluwer Academic Publishers, ISBN 978-1556080104
- Riemann Zeta Function, in Wolfram Mathworld — an explanation with a more mathematical approach
- Tables of selected zeros
- Prime Numbers Get Hitched A general, non-technical description of the significance of the zeta function in relation to prime numbers.
- X-Ray of the Zeta Function Visually oriented investigation of where zeta is real or purely imaginary.
- Formulas and identities for the Riemann Zeta function functions.wolfram.com
- Riemann Zeta Function and Other Sums of Reciprocal Powers, section 23.2 of Abramowitz and Stegun
- Frenkel, Edward. "Million Dollar Math Problem" (video). Brady Haran. Retrieved 11 March 2014.
- Mellin transform and the functional equation of the Riemann Zeta function—Computational examples of Mellin transform methods involving the Riemann Zeta Function