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  "body": "\n## Summary\n\nA monogenic function is a function on an open subset of $\\R^n$ with values in a [[Clifford algebra|A38B1QFK20]] that is annihilated by the [[Dirac operator|3DXGJTEQZH]].\nIt is the higher-dimensional analogue of a holomorphic function and the main object of [[Clifford analysis|DKVSAZQWF7]].\nMonogenic functions satisfy a Cauchy integral formula, have local power series expansions, and their components are harmonic.\n\n## Explanations\n\n### L1 human\n\nA holomorphic function solves the Cauchy–Riemann equations, which can be packed into one equation $\\partial f / \\partial \\bar z = 0$.\nIn $\\R^n$ one packs the derivatives into one operator $\\sum_j e_j \\partial_{x_j}$ with anticommuting units $e_j$.\nA monogenic function is one sent to $0$ by this operator.\nFor example, a constant function is monogenic, and so is $x \\mapsto x / \\abs{x}^n$ away from $0$, where $x = \\sum_j x_j e_j$; this is the Cauchy kernel up to a constant.\n",
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