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  "body": "\n## Summary\n\nA shift operator moves the argument of a function or the index of a sequence by a fixed amount.\nOn functions of a real variable it sends $f$ to $x \\mapsto f(x + h)$; on sequences it sends $(u_n)$ to $(u_{n+1})$.\nIt is the building block of the operator calculus of finite differences, since the forward difference is the shift minus the identity.\nIn functional analysis the shift on sequence spaces is a basic example of a linear operator.\n\n## Explanations\n\n### L1 human\n\nShifting a sequence means dropping its first term and moving every other term one place to the left.\nThe sequence $1, 4, 9, 16, \\dots$ becomes $4, 9, 16, 25, \\dots$.\nFor a function, shifting by $h$ moves its graph $h$ units to the left.\nA linear recurrence such as $u_{n+2} = u_{n+1} + u_n$ can be written with the shift $E$ as $(E^2 - E - I) u = 0$, a polynomial in $E$ applied to $u$.\n",
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