DLMF:9.7.E13 (Q2820)

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Language	Label	Description	Also known as
English	DLMF:9.7.E13	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathrm{Bi}\left(ze^{\pm\pi i/3}\right)\mathrel{% \sim}\sqrt{\frac{2}{\pi}}\frac{e^{\pm\pi i/6}}{z^{1/4}}\*\left(\cos\left(\zeta% -\tfrac{1}{4}\pi\mp\tfrac{1}{2}\mathrm{i}\ln 2\right)\sum_{k=0}^{\infty}(-1)^{% k}\frac{u_{2k}}{\zeta^{2k}}+\sin\left(\zeta-\tfrac{1}{4}\pi\mp\tfrac{1}{2}% \mathrm{i}\ln 2\right)\sum_{k=0}^{\infty}(-1)^{k}\frac{u_{2k+1}}{\zeta^{2k+1}}% \right),}}

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DLMF:9.7.E13

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{\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{2}{3}\pi-\delta}}

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Defining formula

{\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}

C9.S2.SS1.m2addec

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Defining formula

{\displaystyle{\displaystyle\sim}}

C2.S1.SS3.p1.m11ahdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2ajdec

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cosine function

Defining formula

{\displaystyle{\displaystyle\cos\NVar{z}}}

C4.S14.E2.m2addec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2addec

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Defining formula

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

C1.S9.E1.m2adec

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principal branch of logarithm function

Defining formula

{\displaystyle{\displaystyle\ln\NVar{z}}}

C4.S2.E2.m2adec

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Defining formula

{\displaystyle{\displaystyle\operatorname{ph}}}

C1.S9.E7.m1ahdec

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Defining formula

{\displaystyle{\displaystyle\sin\NVar{z}}}

C4.S14.E1.m2addec

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Defining formula

{\displaystyle{\displaystyle k}}

C9.S1.XMD1.m1idec

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Defining formula

{\displaystyle{\displaystyle z}}

C9.S1.XMD3.m1idec

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Defining formula

{\displaystyle{\displaystyle\delta}}

C9.S1.XMD4.m1hdec

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change of variable (locally)

Defining formula

{\displaystyle{\displaystyle\zeta}}

C9.S7.XMD1.m1idec

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Defining formula

{\displaystyle{\displaystyle u_{s}}}

C9.S7.XMD2.m1edec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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