DLMF:10.40.E3 (Q3581): Difference between revisions

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Property / constraint
 

| ph z | 1 2 π - δ phase 𝑧 1 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{2}\pi-\delta}}

|\phase@@{z}|\leq\tfrac{1}{2}\pi-\delta
Property / constraint: | ph z | 1 2 π - δ phase 𝑧 1 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{2}\pi-\delta}} / rank
 
Normal rank

Revision as of 16:39, 30 December 2019

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DLMF:10.40.E3
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    Statements

    I ν ( z ) e z ( 2 π z ) 1 2 k = 0 ( - 1 ) k b k ( ν ) z k , asymptotic-expansion diffop modified-Bessel-first-kind 𝜈 1 𝑧 superscript 𝑒 𝑧 superscript 2 𝜋 𝑧 1 2 superscript subscript 𝑘 0 superscript 1 𝑘 subscript 𝑏 𝑘 𝜈 superscript 𝑧 𝑘 {\displaystyle{\displaystyle I_{\nu}'\left(z\right)\sim\frac{e^{z}}{(2\pi z)^{% \frac{1}{2}}}\sum_{k=0}^{\infty}(-1)^{k}\frac{b_{k}(\nu)}{z^{k}},}}
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    | ph z | 1 2 π - δ phase 𝑧 1 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{2}\pi-\delta}}
    0 references