SymPy Gamma

SymPy:

integrate (x**a*exp (-x),(x,0,oo ))

$\int\limits_{0}^{\infty} x^{a} e^{- x}\, dx$

Antiderivative forms:

Simplify

Integral Steps:

integrate(x**a*exp(-x), (x, 0, oo))

Simplify

Plot:

plot(Piecewise((gamma(a + 1), re(a) > -1), (Integral(x**a*exp(-x), (x, 0, oo)), True)))

Simplify

Roots:

solve(Piecewise((gamma(a + 1), re(a) > -1), (Integral(x**a*exp(-x), (x, 0, oo)), True)), x)

$x =$

Simplify

Derivative:

diff(Piecewise((gamma(a + 1), re(a) > -1), (Integral(x**a*exp(-x), (x, 0, oo)), True)), x)

$\frac{d}{d x} \begin{cases} \Gamma\left(a + 1\right) & \text{for}\: \operatorname{re}{\left(a\right)} > -1 \\\int\limits_{0}^{\infty} x^{a} e^{- x}\, dx & \text{otherwise} \end{cases} =$

Simplify

Antiderivative forms:

Simplify

Series expansion around 0:

series(Piecewise((gamma(a + 1), re(a) > -1), (Integral(x**a*exp(-x), (x, 0, oo)), True)), x, 0, 10)

Simplify

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