Plot of the <a href="https://en.wikipedia.org/wiki/Factorial" class="extiw" title="en:Factorial">factorial</a>, <a href="https://en.wikipedia.org/wiki/Gamma_function" class="extiw" title="en:Gamma function">gamma function</a> and <a href="https://en.wikipedia.org/wiki/Stirling%27s_approximation" class="extiw" title="en:Stirling's approximation">Stirling's approximation</a> in the interval [−0.2, 3.2]:
<dl><dd><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 y_{1}(n)=n!}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>y</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mi>n</mi><mo>!</mo></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle y_{1}(n)=n!}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f473cc56eb63305a6a4fcde8e673a382da5d53a" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:10.537ex; height:2.843ex;" alt="{\displaystyle y_{1}(n)=n!}"></span></dd>
<dd><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 y_{2}(n)=\Gamma (n+1)}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>y</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mi mathvariant="normal">Γ<!-- Γ --></mi><mo stretchy="false">(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle y_{2}(n)=\Gamma (n+1)}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5cead2639db4e00dde57331e3d3f96da3300c004" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:17.156ex; height:2.843ex;" alt="{\displaystyle y_{2}(n)=\Gamma (n+1)}"></span></dd>
<dd><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 y_{3}(n)={\sqrt {2\pi n}}(n/e)^{n}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>y</mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msub><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><msqrt><mn>2</mn><mi>π<!-- π --></mi><mi>n</mi></msqrt></mrow><mo stretchy="false">(</mo><mi>n</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>e</mi><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mi>n</mi></mrow></msup></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle y_{3}(n)={\sqrt {2\pi n}}(n/e)^{n}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/316c05a3eddf957760fb929813ec752980940e5a" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:20.989ex; height:3.176ex;" alt="{\displaystyle y_{3}(n)={\sqrt {2\pi n}}(n/e)^{n}}"></span></dd></dl>
<a href="//commons.wikimedia.org/wiki/User:Geek3" title="User:Geek3">Geek3</a>
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<span class="int-own-work" lang="en">Own work</span>