DLMF:10.15.E4 (Q3150): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2abdec

Revision as of 15:24, 2 January 2020

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DLMF:10.15.E4
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    Statements

    Defining formula
    ∂ ⁡ Y ν ⁡ ( z ) ∂ ⁡ ν | ν = n = - π 2 ⁢ J n ⁡ ( z ) + n ! 2 ⁢ ( 1 2 ⁢ z ) n ⁢ ∑ k = 0 n - 1 ( 1 2 ⁢ z ) k ⁢ Y k ⁡ ( z ) k ! ⁢ ( n - k ) , evaluated-at partial-derivative Bessel-Y-Weber 𝜈 𝑧 𝜈 𝜈 𝑛 𝜋 2 Bessel-J 𝑛 𝑧 𝑛 2 superscript 1 2 𝑧 𝑛 superscript subscript 𝑘 0 𝑛 1 superscript 1 2 𝑧 𝑘 Bessel-Y-Weber 𝑘 𝑧 𝑘 𝑛 𝑘 {\displaystyle{\displaystyle\left.\frac{\partial Y_{\nu}\left(z\right)}{% \partial\nu}\right|_{\nu=n}=-\frac{\pi}{2}J_{n}\left(z\right)+\frac{n!}{2(% \tfrac{1}{2}z)^{n}}\sum_{k=0}^{n-1}\frac{(\tfrac{1}{2}z)^{k}Y_{k}\left(z\right% )}{k!(n-k)},}}
    0 references
    DLMF id
    DLMF:10.15.E4
    0 references
    Symbols used
    Bessel function of the first kind
    Defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2acdec
    0 references
    Bessel function of the second kind
    Defining formula
    Y ν ⁡ ( z ) Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E3.m2abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
     
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