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  "body": "\n## Summary\n\nWZ theory, named after Herbert Wilf and Doron Zeilberger, is a method to prove identities of the form $\\sum_k F(n, k) = 1$ by computer, see the [[definition|4HP429BZQ5]].\nThe proof consists of one rational function, the WZ certificate.\nThe certificate turns $F$ into a Wilf–Zeilberger pair, whose defining equation can be checked by algebra alone.\nIt applies to sums of hypergeometric terms, such as most identities for [[binomial coefficients|0GBZM0MT0F]], and it relates to Zeilberger's algorithm and Gosper's algorithm.\n\n## Explanations\n\n### L1 human\n\nMany identities for sums of binomial coefficients have tricky proofs by hand.\nWZ theory replaces the trick by a mechanical certificate.\nA computer finds a rational function, and anyone can check by simple algebra that it satisfies one equation.\nThat equation forces the sum to be the same for all $n$, so it is enough to check the case $n = 0$.\n",
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