Formula:3654

Digital Library of Mathematical Functions ID 9.12.E28

${\displaystyle{\displaystyle\mathrm{Hi}'\left(z\right)\sim\frac{1}{\pi z^{2}}\sum_{k=0}^{\infty}\frac{(3k+1)!}{k!(3z^{3})^{k}},}}$

Constraint(s)

${\displaystyle{\displaystyle|\operatorname{ph}\left(-z\right)|\leq\tfrac{2}{3}\pi-\delta}}$

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
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\delta}}$: small positive constant
 

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