Formula:3655

Digital Library of Mathematical Functions ID 9.12.E29

${\displaystyle{\displaystyle\mathrm{Hi}\left(z\right)\sim-\frac{1}{\pi z}\sum_{k=0}^{\infty}\frac{(3k)!}{k!(3z^{3})^{k}}+\frac{e^{\zeta}}{\sqrt{\pi}z^{1/4}}\sum_{k=0}^{\infty}\frac{u_{k}}{\zeta^{k}},}}$

Constraint(s)

${\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi-\delta}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{Hi}\left(\NVar{z}\right)}}$: Scorer function (inhomogeneous Airy function)
• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\delta}}$: small positive constant
• ${\displaystyle{\displaystyle\zeta}}$: change of variable (locally)
• ${\displaystyle{\displaystyle u_{s}}}$: expansion coefficient
 

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