DLMF:12.14.E16

MaRDI QIDQ4953

• Label: DLMF:12.14.E16

Digital Library of Mathematical Functions ID 12.14.E16

${\displaystyle{\displaystyle w_{2}(a,x)=xe^{-\frac{1}{4}ix^{2}}M\left(\tfrac{3}{4}-\tfrac{1}{2}ia,\tfrac{3}{2},\tfrac{1}{2}ix^{2}\right)=xe^{\frac{1}{4}ix^{2}}M\left(\tfrac{3}{4}+\tfrac{1}{2}ia,\tfrac{3}{2},-\tfrac{1}{2}ix^{2}\right).}}$

Symbols List

• ${\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}$: $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle a}}$: real or complex parameter
• ${\displaystyle{\displaystyle w_{2}(a,x)}}$: odd solution (locally)
 

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