2.10.E20

MaRDI QIDQ978

• Label: 2.10.E20

Digital Library of Mathematical Functions ID 2.10.E20

${\displaystyle{\displaystyle\sum_{j=0}^{n-1}\frac{x^{j}}{(j!)^{3}}=\frac{1}{2i}\int_{\mathscr{C}}\frac{x^{t}}{(\Gamma\left(t+1\right))^{3}}\cot\left(\pi t\right)\mathrm{d}t,}}$

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
• ${\displaystyle{\displaystyle\cot\NVar{z}}}$: cotangent function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\mathscr{C}}}$: contour
 

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