Formula:980

Digital Library of Mathematical Functions ID 2.10.E22

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \sum_{j=0}^{n-1}\frac{x^{j}}{(j!)^{3}}=\int_{-1/2}^{n-(1/2)}\frac{x^{t}}{(\EulerGamma@{t+1})^{3}}\diff{t}-\int_{\mathscr{C}_{1}}\frac{x^{t}}{(\EulerGamma@{t+1})^{3}}\frac{\diff{t}}{e^{-2\pi it}-1}+\int_{\mathscr{C}_{2}}\frac{x^{t}}{(\EulerGamma@{t+1})^{3}}\frac{\diff{t}}{e^{2\pi it}-1},}

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\mathscr{C}}}$: contour
 

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