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  "body": "\n## Summary\n\nA holonomic function, also called a D-finite function, is a function or [[formal power series|033WGN00BF]] that satisfies a [[linear differential equation|0QQRP17Z7S]] whose coefficients are polynomials.\nMany [[special functions|HWY72ZK273]] are holonomic, for example the exponential, the sine, the logarithm, the [[hypergeometric function|463X5V31D9]] and the [[Bessel functions|CZCMRDWDYW]].\nThe class is closed under sums and products, and the coefficients of a holonomic power series satisfy a [[recurrence|0FYX44GP92]] with polynomial coefficients.\nFor this reason such a differential equation is a finite data structure for the function, which computer algebra uses to prove identities automatically.\n\n## Explanations\n\n### L1 human\n\nSome functions can be described by a short rule that ties the function to its own derivatives.\nA holonomic function is one for which this rule is linear and has polynomials as coefficients.\nFor example $f(x) = e^{x^2}$ satisfies $f'(x) - 2x f(x) = 0$, so it is holonomic.\nKnowing the equation and a few starting values pins down the function completely.\nThe [[gamma function|0H5SYBSED9]] is a well known function that is not holonomic.\n",
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