Formula:6477

Digital Library of Mathematical Functions ID 18.17.E39

${\displaystyle{\displaystyle\int_{0}^{1}P_{2n+1}\left(x\right)x^{z-1}\mathrm{d}x=\frac{(-1)^{n}{\left(1-\frac{1}{2}z\right)_{n}}}{2{\left(\frac{1}{2}+\frac{1}{2}z\right)_{n+1}}},}}$

Constraint(s)

${\displaystyle{\displaystyle\Re z>-1}}$

Symbols List

• ${\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}$: Legendre polynomial
• ${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$:
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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