DLMF:10.15.E3 (Q3149): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11429 / rank
 
Normal rank
Property / Symbols used: Q11429 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11429 / qualifier
 
xml-id: C10.S1.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q11428 / rank
 
Normal rank
Property / Symbols used: Q11428 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11428 / qualifier
 
xml-id: C10.S1.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: Q11426 / rank
 
Normal rank
Property / Symbols used: Q11426 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11426 / qualifier
 
xml-id: C10.S1.XMD6.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1bdec

Latest revision as of 15:24, 2 January 2020

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DLMF:10.15.E3
No description defined

    Statements

    Defining formula
    ∂ ⁡ J ν ⁡ ( z ) ∂ ⁡ ν | ν = n = π 2 ⁢ Y n ⁡ ( z ) + n ! 2 ⁢ ( 1 2 ⁢ z ) n ⁢ ∑ k = 0 n - 1 ( 1 2 ⁢ z ) k ⁢ J k ⁡ ( z ) k ! ⁢ ( n - k ) . evaluated-at partial-derivative Bessel-J 𝜈 𝑧 𝜈 𝜈 𝑛 𝜋 2 Bessel-Y-Weber 𝑛 𝑧 𝑛 2 superscript 1 2 𝑧 𝑛 superscript subscript 𝑘 0 𝑛 1 superscript 1 2 𝑧 𝑘 Bessel-J 𝑘 𝑧 𝑘 𝑛 𝑘 {\displaystyle{\displaystyle\left.\frac{\partial J_{\nu}\left(z\right)}{% \partial\nu}\right|_{\nu=n}=\frac{\pi}{2}Y_{n}\left(z\right)+\frac{n!}{2(% \tfrac{1}{2}z)^{n}}\sum_{k=0}^{n-1}\frac{(\tfrac{1}{2}z)^{k}J_{k}\left(z\right% )}{k!(n-k)}.}}
    0 references
    DLMF id
    DLMF:10.15.E3
    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.m2abdec
    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.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    partial derivative of $$f$$ with respect to $$x$$
    Defining formula
    ∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
    xml-id
    C1.S5.E3.m4abdec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2abdec
    0 references
    Q11429
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1dec
    0 references
    Q11428
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1adec
    0 references
    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1bdec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1bdec
    0 references
     
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