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- Q282649 description "mathematischer Satz aus der Zahlentheorie" @default.
- Q282649 description "theorem" @default.
- Q282649 name "Pentagonal number theorem" @default.
- Q282649 name "Pentagonalzahlensatz" @default.
- Q282649 name "Teorema dei numeri pentagonali" @default.
- Q282649 name "pentagonal number theorem" @default.
- Q282649 name "teorema del número pentagonal" @default.
- Q282649 name "teoremo pri kvinangulaj nombroj" @default.
- Q282649 name "théorème du nombre pentagonal" @default.
- Q282649 name "Пентагональная теорема Эйлера" @default.
- Q282649 name "משפט המספרים המחומשים" @default.
- Q282649 name "オイラーの五角数定理" @default.
- Q282649 name "五邊形數定理" @default.
- Q282649 name "五邊形數定理" @default.
- Q282649 name "오일러의 오각수 정리" @default.
- Q282649 type Item @default.
- Q282649 label "Pentagonal number theorem" @default.
- Q282649 label "Pentagonalzahlensatz" @default.
- Q282649 label "Teorema dei numeri pentagonali" @default.
- Q282649 label "pentagonal number theorem" @default.
- Q282649 label "teorema del número pentagonal" @default.
- Q282649 label "teoremo pri kvinangulaj nombroj" @default.
- Q282649 label "théorème du nombre pentagonal" @default.
- Q282649 label "Пентагональная теорема Эйлера" @default.
- Q282649 label "משפט המספרים המחומשים" @default.
- Q282649 label "オイラーの五角数定理" @default.
- Q282649 label "五邊形數定理" @default.
- Q282649 label "五邊形數定理" @default.
- Q282649 label "오일러의 오각수 정리" @default.
- Q282649 altLabel "Teorema del numero pentagonal" @default.
- Q282649 prefLabel "Pentagonal number theorem" @default.
- Q282649 prefLabel "Pentagonalzahlensatz" @default.
- Q282649 prefLabel "Teorema dei numeri pentagonali" @default.
- Q282649 prefLabel "pentagonal number theorem" @default.
- Q282649 prefLabel "teorema del número pentagonal" @default.
- Q282649 prefLabel "teoremo pri kvinangulaj nombroj" @default.
- Q282649 prefLabel "théorème du nombre pentagonal" @default.
- Q282649 prefLabel "Пентагональная теорема Эйлера" @default.
- Q282649 prefLabel "משפט המספרים המחומשים" @default.
- Q282649 prefLabel "オイラーの五角数定理" @default.
- Q282649 prefLabel "五邊形數定理" @default.
- Q282649 prefLabel "五邊形數定理" @default.
- Q282649 prefLabel "오일러의 오각수 정리" @default.
- Q282649 P2534 Q282649-f4e1befe-4d79-9afe-f0e7-bc94558a8bf2 @default.
- Q282649 P2812 Q282649-B1E5B20D-345C-4E3F-BDC4-2186C3305DA6 @default.
- Q282649 P31 Q282649-A76FF4FA-A5CD-42BA-A728-7CA70C75561C @default.
- Q282649 P6104 Q282649-15EEFBB5-67CF-4F5D-A568-1AAE7B831F99 @default.
- Q282649 P6366 Q282649-89F58AEA-A85E-4C57-9A74-29801E802568 @default.
- Q282649 P646 Q282649-411BB7CC-3B90-4720-A0DC-891C9E5BC05D @default.
- Q282649 P6366 34140744 @default.
- Q282649 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \prod _{n=1}^{\infty }\left(1-x^{n}\right)=\sum _{k=-\infty }^{\infty }\left(-1\right)^{k}x^{k\left(3k-1\right)/2}=1+\sum _{k=1}^{\infty }(-1)^{k}\left(x^{k(3k+1)/2}+x^{k(3k-1)/2}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∏<!-- ∏ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </munderover> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−<!-- − --></mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mo>−<!-- − --></mo> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </munderover> <msup> <mrow> <mo>(</mo> <mrow> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msup> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mrow> <mo>(</mo> <mrow> <mn>3</mn> <mi>k</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>1</mn> <mo>+</mo> <munderover> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </munderover> <mo stretchy="false">(</mo> <mo>−<!-- − --></mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo stretchy="false">(</mo> <mn>3</mn> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo stretchy="false">(</mo> <mn>3</mn> <mi>k</mi> <mo>−<!-- − --></mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \prod _{n=1}^{\infty }\left(1-x^{n}\right)=\sum _{k=-\infty }^{\infty }\left(-1\right)^{k}x^{k\left(3k-1\right)/2}=1+\sum _{k=1}^{\infty }(-1)^{k}\left(x^{k(3k+1)/2}+x^{k(3k-1)/2}\right)}</annotation> </semantics> </math>" @default.
- Q282649 P2812 "PentagonalNumberTheorem" @default.
- Q282649 P31 Q65943 @default.
- Q282649 P6104 Q8487137 @default.
- Q282649 P6366 "34140744" @default.
- Q282649 P646 "/m/01x_mc" @default.