Animation of the partial sums of the Dirichlet kernel terms <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 D_{n}(x)={\frac {1}{2L}}{\frac {\operatorname {sen} \left(n+{\frac {1}{2}}\right){\frac {\pi x}{L}}}{\operatorname {sen} {\frac {\pi x}{2L}}}}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>D</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mrow><mn>2</mn><mi>L</mi></mrow></mfrac></mrow><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mi>sen</mi><mo>⁡<!-- ⁡ --></mo><mrow><mo>(</mo><mrow><mi>n</mi><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mrow><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mi>π<!-- π --></mi><mi>x</mi></mrow><mi>L</mi></mfrac></mrow></mrow><mrow><mi>sen</mi><mo>⁡<!-- ⁡ --></mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mi>π<!-- π --></mi><mi>x</mi></mrow><mrow><mn>2</mn><mi>L</mi></mrow></mfrac></mrow></mrow></mfrac></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle D_{n}(x)={\frac {1}{2L}}{\frac {\operatorname {sen} \left(n+{\frac {1}{2}}\right){\frac {\pi x}{L}}}{\operatorname {sen} {\frac {\pi x}{2L}}}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b09d7cd0fa1b3efb808abb63da25f87419867ad" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.005ex; width:27.78ex; height:7.676ex;" alt="{\displaystyle D_{n}(x)={\frac {1}{2L}}{\frac {\operatorname {sen} \left(n+{\frac {1}{2}}\right){\frac {\pi x}{L}}}{\operatorname {sen} {\frac {\pi x}{2L}}}}}"></span>
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