Formula:3316

Digital Library of Mathematical Functions ID 8.12.E16

${\displaystyle{\displaystyle\frac{e^{\pm\pi ia}}{2i\sin\left(\pi a\right)}Q\left(-a,ae^{\pm\pi i}\right)\sim\pm\frac{1}{2}-\frac{i}{\sqrt{2\pi a}}\sum_{k=0}^{\infty}c_{k}(0)(-a)^{-k},}}$

Constraint(s)

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

Symbols List

• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle Q\left(\NVar{a},\NVar{z}\right)}}$: normalized incomplete gamma function
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle a}}$: parameter
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle\delta}}$: small positive constant
• ${\displaystyle{\displaystyle c_{k}(\eta)}}$: coefficients
 

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