Formula:4878

Digital Library of Mathematical Functions ID 12.10.E19

${\displaystyle{\displaystyle U'\left(-\tfrac{1}{2}\mu^{2},\mu t\sqrt{2}\right)\sim\mu\sqrt{2}g(\mu)(1-t^{2})^{\frac{1}{4}}\*\left(\sin\kappa\sum_{s=0}^{\infty}(-1)^{s}\frac{\widetilde{\cal{B}}_{2s}(t)}{\mu^{4s}}+\cos\kappa\sum_{s=0}^{\infty}(-1)^{s}\frac{\widetilde{\cal{B}}_{2s+1}(t)}{\mu^{4s+2}}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle s}}$: nonnegative integer
• ${\displaystyle{\displaystyle\kappa}}$: κ
• ${\displaystyle{\displaystyle\widetilde{\mathcal{B}}_{s}(t)}}$: coefficients
• ${\displaystyle{\displaystyle g(\mu)}}$: expansion (locally)
 

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