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  "body": "\n## Definition\n\nThe hyperbolic cosine is the function $\\cosh \\colon \\mathbb{R} \\to \\mathbb{R}$ defined by\n$$\\cosh x = \\frac{e^x + e^{-x}}{2}.$$\n\n## Remarks\n\nIt is even, and $\\cosh x \\ge 1$, with equality only at $x = 0$.\nIts power series is $\\cosh x = \\sum_{n=0}^{\\infty} \\frac{x^{2n}}{(2n)!}$.\nThe graph of $\\cosh$ is the catenary, the shape of a hanging chain. Mathlib defines it as `Real.cosh`.\n\n## Explanations\n\n### L1 human\n\nThe hyperbolic cosine is the even part of $e^x$.\nIts graph looks like a parabola near $0$, but it grows exponentially.\n",
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