DLMF:12.7.E14 (Q4137): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:12.7.E14	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle U\left(a,z\right)=2^{-\frac{1}{4}-\frac{1}{2}a}e^% {-\frac{1}{4}z^{2}}U\left(\tfrac{1}{2}a+\tfrac{1}{4},\tfrac{1}{2},\tfrac{1}{2}% z^{2}\right)=2^{-\frac{3}{4}-\frac{1}{2}a}ze^{-\frac{1}{4}z^{2}}U\left(\tfrac{% 1}{2}a+\tfrac{3}{4},\tfrac{3}{2},\tfrac{1}{2}z^{2}\right)=2^{-\frac{1}{2}a}z^{% -\frac{1}{2}}W_{-\frac{1}{2}a,\pm\frac{1}{4}}\left(\tfrac{1}{2}z^{2}\right).}}

0 references

DLMF:12.7.E14

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Kummer confluent hypergeometric function

Defining formula

{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}

C13.S2.E6.m2adec

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Whittaker confluent hypergeometric function

Defining formula

{\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}

C13.S14.E3.m2adec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2aidec

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Defining formula

{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}

C12.S2.SS1.p1.m1aidec

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Defining formula

{\displaystyle{\displaystyle z}}

C12.S1.XMD3.m1mdec

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Sitelinks

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