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Display information for equation id:math.224631.17 on revision:224631

* Page found: Stirling's approximation (eq math.224631.17)

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Hash: 1f1180d5219a3bf04549683eb077a837

TeX (original user input):

n! = e^{y} \sqrt{n} \left( \frac{n}{e} \right)^n \left( 1 + O \left( \frac{1}{n} \right) \right).

TeX (checked):

n!=e^{y}{\sqrt {n}}\left({\frac {n}{e}}\right)^{n}\left(1+O\left({\frac {1}{n}}\right)\right).

LaTeXML (experimental; uses MathML) rendering

MathML (6.184 KB / 1.115 KB) :

n ! = e y n ( n e ) n ( 1 + O ( 1 n ) ) . 𝑛 superscript 𝑒 𝑦 𝑛 superscript 𝑛 𝑒 𝑛 1 𝑂 1 𝑛 {\displaystyle n!=e^{{y}}{\sqrt{n}}\left({\frac{n}{e}}\right)^{n}\left(1+O% \left({\frac{1}{n}}\right)\right).}
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SVG (10.335 KB / 3.582 KB) :

n factorial equals e Superscript y Baseline times StartRoot n EndRoot times left-parenthesis StartFraction n Over e EndFraction right-parenthesis Superscript n Baseline times left-parenthesis 1 plus upper O times left-parenthesis StartFraction 1 Over n EndFraction right-parenthesis right-parenthesis period

SVG (MathML can be enabled via browser plugin) rendering

MathML (1.589 KB / 435 B) :

n ! = e y n ( n e ) n ( 1 + O ( 1 n ) ) . {\displaystyle n!=e^{y}{\sqrt {n}}\left({\frac {n}{e}}\right)^{n}\left(1+O\left({\frac {1}{n}}\right)\right).}
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SVG (7.91 KB / 3.214 KB) :

{\displaystyle n!=e^{y}{\sqrt {n}}\left({\frac {n}{e}}\right)^{n}\left(1+O\left({\frac {1}{n}}\right)\right).}

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