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<a class="decoration-primary-500 hover:underline hover:decoration-2 hover:underline-offset-2" rel=me href=/>stemformulas</a></div><ul class="flex list-none flex-col ltr:text-right rtl:text-left sm:flex-row"><li class="group mb-1 sm:mb-0 sm:me-7 sm:last:me-0.5"><a class="decoration-primary-500 hover:underline hover:decoration-2 hover:underline-offset-2" href=/formulas/ title=formulas>formulas</a></li><li class="group mb-1 sm:mb-0 sm:me-7 sm:last:me-0.5"><a class="decoration-primary-500 hover:underline hover:decoration-2 hover:underline-offset-2" href=/tags/ title=Tags>tags</a></li><li class="group mb-1 sm:mb-0 sm:me-7 sm:last:me-0.5"><a class="decoration-primary-500 hover:underline hover:decoration-2 hover:underline-offset-2" href=/about/ title=about>about</a></li><li class="group mb-1 sm:mb-0 sm:me-7 sm:last:me-0.5"><a class="decoration-primary-500 hover:underline hover:decoration-2 hover:underline-offset-2" href=/suggest/ title=Suggest>suggest</a></li><li class="group mb-1 sm:mb-0 sm:me-7 sm:last:me-0.5"><a class="decoration-primary-500 hover:underline hover:decoration-2 hover:underline-offset-2" href=https://github.com/stemformulas/stemformulas.github.io/ title>github</a></li><li class="ltr:sm:mr-7 ltr:sm:last:mr-0 rtl:sm:ml-7 rtl:sm:last:ml-0"><button id=search-button class="text-base hover:text-primary-600 dark:hover:text-primary-400" title="Search (/)">
<span class="relative inline-block align-text-bottom px-1 icon"><svg aria-hidden="true" focusable="false" data-prefix="fas" data-icon="search" class="svg-inline--fa fa-search fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentcolor" d="M505 442.7 405.3 343c-4.5-4.5-10.6-7-17-7H372c27.6-35.3 44-79.7 44-128C416 93.1 322.9.0 208 0S0 93.1.0 208s93.1 208 208 208c48.3.0 92.7-16.4 128-44v16.3c0 6.4 2.5 12.5 7 17l99.7 99.7c9.4 9.4 24.6 9.4 33.9.0l28.3-28.3c9.4-9.4 9.4-24.6.1-34zM208 336c-70.7.0-128-57.2-128-128 0-70.7 57.2-128 128-128 70.7.0 128 57.2 128 128 0 70.7-57.2 128-128 128z"/></svg></span></button></li></ul></nav></header><div class="relative flex flex-col grow"><main id=main-content class=grow><article><header class=max-w-prose><h1 class="mt-0 text-4xl font-extrabold text-neutral-900 dark:text-neutral">Error Function</h1><div class="mt-8 mb-12 text-base text-neutral-500 dark:text-neutral-400 print:hidden"><div class="my-2 text-xs text-neutral-500 dark:text-neutral-400"><a href=/tags/mathematics/ class="rounded-md border border-neutral-200 px-2 py-[1px] hover:border-black hover:text-primary-700 dark:border-neutral-600 dark:hover:border-primary-600 dark:hover:text-primary-400">mathematics</a>
<a href=/tags/statistics/ class="rounded-md border border-neutral-200 px-2 py-[1px] hover:border-black hover:text-primary-700 dark:border-neutral-600 dark:hover:border-primary-600 dark:hover:text-primary-400">statistics</a></div><div class="ml-1 flex flex-row flex-wrap items-center"><time datetime="2024-02-14 00:00:00 +0000 UTC">Added on&nbsp;Feb 14 2024</time></div></div></header><section class="flex flex-col max-w-full mt-0 prose dark:prose-invert lg:flex-row"><div class="order-first px-0 lg:order-last lg:max-w-xs lg:ps-8"><div class="toc pe-5 print:hidden lg:sticky lg:top-10"><details open class="-ms-5 mt-0 overflow-hidden rounded-lg ps-5"><summary class="-ms-5 block cursor-pointer bg-neutral-100 py-1 ps-5 text-lg font-semibold text-neutral-800 dark:bg-neutral-700 dark:text-neutral-100 lg:hidden">Table of Contents</summary><div class="-ms-5 border-s border-dotted border-neutral-300 py-2 ps-5 dark:border-neutral-600"><nav id=TableOfContents><ul><li><a href=#sources>Sources</a></li></ul></nav></div></details></div></div><div class="min-w-0 min-h-0 max-w-prose grow"><p>The error function, often used in statistics and probability, is defined as the integral of the Gaussian function. It is defined as follows:</p><p>$$ \text{erf}(z) = \frac{2}{\sqrt{\pi}} \int_0^z e^{-t^2} dt $$</p><h2 id=sources class="relative group">Sources <span class="absolute top-0 w-6 transition-opacity opacity-0 -start-6 not-prose group-hover:opacity-100"><a class="group-hover:text-primary-300 dark:group-hover:text-neutral-700" style=text-decoration-line:none!important href=#sources aria-label=Anchor>#</a></span></h2><ul><li><a href=https://en.wikipedia.org/wiki/Error_function target=_blank rel="noreferrer noopener">Wikipedia</a></li></ul></div></section><footer class="pt-8 max-w-prose print:hidden"><div class=pt-8><hr class="border-dotted border-neutral-300 dark:border-neutral-600"><div class="flex justify-between pt-3"><span><a class="group flex" href=/formulas/bernoullis-principle/><span class="me-2 text-neutral-700 transition-transform group-hover:-translate-x-[2px] group-hover:text-primary-600 dark:text-neutral dark:group-hover:text-primary-400"><span class="ltr:inline rtl:hidden">&larr;</span><span class="ltr:hidden rtl:inline">&rarr;</span></span>
<span class="flex flex-col"><span class="mt-[0.1rem] leading-6 group-hover:underline group-hover:decoration-primary-500">Bernoulli's Principle</span>
<span class="mt-[0.1rem] text-xs text-neutral-500 dark:text-neutral-400"><time datetime="2024-02-07 00:00:00 +0000 UTC">Added on&nbsp;Feb 7 2024</time></span></span></a></span>
<span><a class="group flex text-right" href=/formulas/snells-law/><span class="flex flex-col"><span class="mt-[0.1rem] leading-6 group-hover:underline group-hover:decoration-primary-500">Snell's Law</span>
<span class="mt-[0.1rem] text-xs text-neutral-500 dark:text-neutral-400"><time datetime="2024-02-16 00:00:00 +0000 UTC">Added on&nbsp;Feb 16 2024</time></span></span>
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