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  "body": "\n## Summary\n\nA Blaschke product is a bounded [[holomorphic function|0DG0Z72CQD]] on the [[unit disc|8G5ABXRK85]] built as a product of disc automorphisms, one for each prescribed zero.\nIt exists exactly when the zeros satisfy the Blaschke condition $\\sum_n (1 - \\abs{a_n}) \u003c \\infty$.\nBlaschke products are the basic [[inner functions|NN8XH5RJYB]], and every nonzero function in a [[Hardy space|PNNNFJVF6W]] factors through the Blaschke product of its zeros.\n\n## Explanations\n\n### L1 human\n\nEach factor $\\frac{\\abs{a}}{a} \\frac{a - z}{1 - \\bar a z}$ is a [[Möbius transformation|0B346DDAM5]] that maps the disc onto itself and vanishes only at $a$.\nMultiplying such factors gives a function with exactly the chosen zeros and with modulus at most $1$.\nWith infinitely many zeros, the product converges only if the zeros approach the circle fast enough.\nFor example, the zeros $a_n = 1 - 2^{-n}$ are allowed, since $\\sum 2^{-n} \u003c \\infty$.\nThe zeros $a_n = 1 - 1/n$ are not allowed, since $\\sum 1/n = \\infty$.\n",
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