DLMF:10.40.E4 (Q3582): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2acdec

Revision as of 13:53, 2 January 2020

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DLMF:10.40.E4
No description defined

    Statements

    Defining formula
    K ν ′ ⁡ ( z ) ∼ - ( π 2 ⁢ z ) 1 2 ⁢ e - z ⁢ ∑ k = 0 ∞ b k ⁢ ( ν ) z k , asymptotic-expansion diffop modified-Bessel-second-kind 𝜈 1 𝑧 superscript 𝜋 2 𝑧 1 2 superscript 𝑒 𝑧 superscript subscript 𝑘 0 subscript 𝑏 𝑘 𝜈 superscript 𝑧 𝑘 {\displaystyle{\displaystyle K_{\nu}'\left(z\right)\sim-\left(\frac{\pi}{2z}% \right)^{\frac{1}{2}}e^{-z}\sum_{k=0}^{\infty}\frac{b_{k}(\nu)}{z^{k}},}}
    0 references
    DLMF id
    DLMF:10.40.E4
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    constraint
    | ph ⁡ z | ≤ 3 2 ⁢ π - δ phase 𝑧 3 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{3}{2}\pi-\delta}}
    0 references
    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
     
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