DLMF:12.2.E19 (Q4104)

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Language	Label	Description	Also known as
English	DLMF:12.2.E19	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle U\left(a,z\right)=\pm ie^{\pm i\pi a}U\left(a,-z% \right)+\frac{\sqrt{2\pi}}{\Gamma\left(\tfrac{1}{2}+a\right)}e^{\pm i\pi(\frac% {1}{2}a-\frac{1}{4})}U\left(-a,\pm iz\right).}}

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DLMF:12.2.E19

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Defining formula

{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.m2aidec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2akdec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2acdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{i}}}

C1.S9.E1.m2acdec

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Defining formula

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

C12.S2.SS1.p1.m1akdec

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Defining formula

{\displaystyle{\displaystyle z}}

C12.S1.XMD3.m1ndec

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Defining formula

{\displaystyle{\displaystyle a}}

C12.S1.XMD6.m1kdec

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