SymPy Gamma

SymPy:

series (1/x,x,10000)

$\mathrm{series}(\frac{1}{x}, x, 10000)$

Result:

$\frac{1}{5000} + \frac{\left(x - 10000\right)^{2}}{1000000000000} - \frac{\left(x - 10000\right)^{3}}{10000000000000000} + \frac{\left(x - 10000\right)^{4}}{100000000000000000000} - \frac{\left(x - 10000\right)^{5}}{1000000000000000000000000} - \frac{x}{100000000} + O\left(\left(x - 10000\right)^{6}; x\rightarrow 10000\right)$

Simplification:

3/5000 - 3*x/20000000 + x**2/50000000000 - 3*x**3/2000000000000000 + 3*x**4/50000000000000000000 - x**5/1000000000000000000000000 + O((x - 10000)**6, (x, 10000))

$\frac{3}{5000} - \frac{3 x}{20000000} + \frac{x^{2}}{50000000000} - \frac{3 x^{3}}{2000000000000000} + \frac{3 x^{4}}{50000000000000000000} - \frac{x^{5}}{1000000000000000000000000} + O\left(\left(x - 10000\right)^{6}; x\rightarrow 10000\right)$

Plot:

Roots:

solve(1/5000 + (x - 10000)**2/1000000000000 - (x - 10000)**3/10000000000000000 + (x - 10000)**4/100000000000000000000 - (x - 10000)**5/1000000000000000000000000 - x/100000000 + O((x - 10000)**6, (x, 10000)), x)

$x =$

Derivative:

diff(1/5000 + (x - 10000)**2/1000000000000 - (x - 10000)**3/10000000000000000 + (x - 10000)**4/100000000000000000000 - (x - 10000)**5/1000000000000000000000000 - x/100000000 + O((x - 10000)**6, (x, 10000)), x)

$\frac{d}{d x} \left(\frac{1}{5000} + \frac{\left(x - 10000\right)^{2}}{1000000000000} - \frac{\left(x - 10000\right)^{3}}{10000000000000000} + \frac{\left(x - 10000\right)^{4}}{100000000000000000000} - \frac{\left(x - 10000\right)^{5}}{1000000000000000000000000} - \frac{x}{100000000} + O\left(\left(x - 10000\right)^{6}; x\rightarrow 10000\right)\right) =$

Antiderivative forms:

Series expansion around 0:

series(1/5000 + (x - 10000)**2/1000000000000 - (x - 10000)**3/10000000000000000 + (x - 10000)**4/100000000000000000000 - (x - 10000)**5/1000000000000000000000000 - x/100000000 + O((x - 10000)**6, (x, 10000)), x, 0, 10)

See what Wolfram|Alpha has to say.

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