Asymptotic expansions of the sine function

Thread starter Robin04
Start date Jul 14, 2019
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Function Sine

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The discussion focuses on asymptotic expansions of the sine function, specifically exploring the first-order Taylor series expansion where \( f_1(a) = a \) and \( f_2(b) = b \). Participants question the existence of alternative solutions and the applicability of the Bhaskara formula in this context. The conversation emphasizes the need for clarity regarding the limits of the asymptotic expansions being considered.

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Jul 14, 2019

Robin04

Homework Statement: ##\sin{(a + b)}\sim f_1(a)+f_2(b)##

Relevant Equations: -

There are no restrictions for ##a,b,f_1,f_2##. One solution is the first order Taylor series expansion of course with ##f_1(a)=a,f_2(b)=b##, but are there any other solutions? I tried the Bhaskara formula but I couldn't express it in this form.

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Jul 14, 2019

pasmith

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Asymptotic in what limit?

Jul 14, 2019

Robin04

pasmith said:

Asymptotic in what limit?

Depends on the expansion, it's not specified at this point yet.

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