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  "body": "\n## Definition\n\nThe hyperbolic sine is the function $\\sinh \\colon \\mathbb{R} \\to \\mathbb{R}$ defined by\n$$\\sinh x = \\frac{e^x - e^{-x}}{2}.$$\n\n## Remarks\n\nIt is odd and strictly increasing, and it is a bijection of $\\mathbb{R}$ onto $\\mathbb{R}$.\nIts power series is $\\sinh x = \\sum_{n=0}^{\\infty} \\frac{x^{2n+1}}{(2n+1)!}$, the sine series without the signs.\nMathlib defines it as `Real.sinh`.\n\n## Explanations\n\n### L1 human\n\nThe hyperbolic sine is the odd part of $e^x$.\nFor large $x$, it is close to $e^x / 2$.\n",
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