Formula:10639

Digital Library of Mathematical Functions ID 36.8.E3

${\displaystyle{\displaystyle\dfrac{3^{2/3}}{4\pi^{2}}\Psi^{(\mathrm{H})}\left(3^{1/3}\mathbf{x}\right)=\mathrm{Ai}\left(x\right)\mathrm{Ai}\left(y\right)\sum\limits_{n=0}^{\infty}(-3^{-1/3}iz)^{n}\dfrac{c_{n}(x)c_{n}(y)}{n!}+\mathrm{Ai}\left(x\right)\mathrm{Ai}'\left(y\right)\sum\limits_{n=2}^{\infty}(-3^{-1/3}iz)^{n}\dfrac{c_{n}(x)d_{n}(y)}{n!}+\mathrm{Ai}'\left(x\right)\mathrm{Ai}\left(y\right)\sum\limits_{n=2}^{\infty}(-3^{-1/3}iz)^{n}\dfrac{d_{n}(x)c_{n}(y)}{n!}+\mathrm{Ai}'\left(x\right)\mathrm{Ai}'\left(y\right)\sum\limits_{n=1}^{\infty}(-3^{-1/3}iz)^{n}\dfrac{d_{n}(x)d_{n}(y)}{n!},}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\Psi^{(\mathrm{H})}\left(\NVar{\mathbf{x}}\right)}}$: hyperbolic umbilic canonical integral function
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle y}}$: real parameter
• ${\displaystyle{\displaystyle z}}$: real parameter
• ${\displaystyle{\displaystyle m}}$: integer
• ${\displaystyle{\displaystyle x}}$: real parameter
• ${\displaystyle{\displaystyle c_{n}(t)}}$: coefficients
• ${\displaystyle{\displaystyle d_{n}(t)}}$: coefficients
 

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