SymPy Gamma

SymPy:

series (sin (x),x,pi /2)

$\mathrm{series}(\mathrm{sin}(x), x, \frac{\pi}{2})$

Result:

$1 - \frac{\left(x - \frac{\pi}{2}\right)^{2}}{2} + \frac{\left(x - \frac{\pi}{2}\right)^{4}}{24} + O\left(\left(x - \frac{\pi}{2}\right)^{6}; x\rightarrow \frac{\pi}{2}\right)$

Simplification:

O(1, (x, pi/2))

$O\left(1; x\rightarrow \frac{\pi}{2}\right)$

Plot:

Roots:

solve(1 - (x - pi/2)**2/2 + (x - pi/2)**4/24 + O((x - pi/2)**6, (x, pi/2)), x)

$x =$

Derivative:

diff(1 - (x - pi/2)**2/2 + (x - pi/2)**4/24 + O((x - pi/2)**6, (x, pi/2)), x)

$\frac{d}{d x} \left(1 - \frac{\left(x - \frac{\pi}{2}\right)^{2}}{2} + \frac{\left(x - \frac{\pi}{2}\right)^{4}}{24} + O\left(\left(x - \frac{\pi}{2}\right)^{6}; x\rightarrow \frac{\pi}{2}\right)\right) =$

Antiderivative forms:

Series expansion around 0:

series(1 - (x - pi/2)**2/2 + (x - pi/2)**4/24 + O((x - pi/2)**6, (x, pi/2)), x, 0, 10)

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