Formula:744

Digital Library of Mathematical Functions ID 2.4.E19

${\displaystyle{\displaystyle I(\alpha,z)=e^{-cz}\int_{\mathscr{Q}}\exp\left(-z\left(\tfrac{1}{3}w^{3}+aw^{2}+bw\right)\right)f(\alpha,w)\mathrm{d}w,}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\exp\NVar{z}}}$: exponential function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle I(\alpha,z)}}$: integral
• ${\displaystyle{\displaystyle w}}$: change of variable
• ${\displaystyle{\displaystyle a}}$: a
• ${\displaystyle{\displaystyle b}}$: b
• ${\displaystyle{\displaystyle\mathscr{Q}}}$: countour
• ${\displaystyle{\displaystyle f(\alpha,w)}}$: function
• ${\displaystyle{\displaystyle c}}$: real constant
 

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