Logarithmic growth rate of the Bernoulli numbers of even index.
Solid blue graph shows <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \log |B_{\lfloor 2k\rfloor }|}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>log</mi><mo>⁡<!-- ⁡ --></mo><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow><msub><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mo fence="false" stretchy="false">⌊<!-- ⌊ --></mo><mn>2</mn><mi>k</mi><mo fence="false" stretchy="false">⌋<!-- ⌋ --></mo></mrow></msub><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \log |B_{\lfloor 2k\rfloor }|}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c12b99482e5a8d5a8177e651b54f7008641db4a" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.171ex; width:9.787ex; height:3.176ex;" alt="{\displaystyle \log |B_{\lfloor 2k\rfloor }|}"></span>, dotted red graph shows the asymptotic estimate <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \log \left(4{\sqrt {\pi k}}\left({\frac {k}{\pi e}}\right)^{2k}\right)}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>log</mi><mo>⁡<!-- ⁡ --></mo><mrow><mo>(</mo><mrow><mn>4</mn><mrow class="MJX-TeXAtom-ORD"><msqrt><mi>π<!-- π --></mi><mi>k</mi></msqrt></mrow><msup><mrow><mo>(</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>k</mi><mrow><mi>π<!-- π --></mi><mi>e</mi></mrow></mfrac></mrow><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mn>2</mn><mi>k</mi></mrow></msup></mrow><mo>)</mo></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \log \left(4{\sqrt {\pi k}}\left({\frac {k}{\pi e}}\right)^{2k}\right)}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59b7f630637ae01d1b89cdbe155ce10a2ab08710" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.171ex; width:20.878ex; height:7.509ex;" alt="{\displaystyle \log \left(4{\sqrt {\pi k}}\left({\frac {k}{\pi e}}\right)^{2k}\right)}"></span>.
No machine-readable author provided. <a href="//commons.wikimedia.org/wiki/User:Fredrik" title="User:Fredrik">Fredrik</a> assumed (based on copyright claims).
17 May 2006 (original upload date)
No machine-readable source provided. Own work assumed (based on copyright claims).