An approach to finding a compositional square root is to posit a power series for f of the form f ( x ) = a 0 + a 1 x + a 2 x 2 + a 3 x 3 + ⋯ and then use the ...
Mar 11, 2019 · Let's say rin(x) is the functional square root of sin(x) (that is to say rin(rin(x))=sin(x)). rin(x) can be approximated by f(x). An even better ...
The natural question is whether there is a differentiable, perhaps infinitely differentiable, solution on the real line. The source paper refers to notes of ...
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Finding a Compositional Square Root of Sine - Taylor & Francis Online
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As a young undergraduate, the second author—as a self-prescribed test to decide if he should pursue a career in mathematics—considered the following ...
Feb 21, 2024 · We consider the following type of problem: Given a function g:A→A, find a function f:A→A such that g=f°f. We are especially interested in ...
Feb 12, 2020 · 1 Answer 1 ... Functional square root of sine is not unique, and it cannot be defined in the whole complex plane (according to a theorem of I. N. ...
Nov 22, 2022 · ... sin x for all real x. In other words, find a compositional square root of the sine function. Dear reader, since you are finding this account ...
Jun 15, 2021 · Step 3: Taking square roots on both sides. Step 4: Find the value of x by taking inverse trigonometric functions. Equations and Definitions for ...
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Posted: Aug 10, 2021
Posted: Aug 10, 2021
In mathematics, a functional square root is a square root of a function with respect to the operation of function composition. In other words, a functional ...