DLMF:10.65.E7 (Q3840)

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DLMF:10.65.E7
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    Statements

    test
    ber ν ⁡ x ⁢ bei ν ′ ⁡ x - ber ν ′ ⁡ x ⁢ bei ν ⁡ x = ( 1 2 ⁢ x ) 2 ⁢ ν + 1 ⁢ ∑ k = 0 ∞ 1 Γ ⁡ ( ν + k + 1 ) ⁢ Γ ⁡ ( ν + 2 ⁢ k + 2 ) ⁢ ( 1 4 ⁢ x 2 ) 2 ⁢ k k ! , Kelvin-ber 𝜈 𝑥 diffop Kelvin-bei 𝜈 1 𝑥 diffop Kelvin-ber 𝜈 1 𝑥 Kelvin-bei 𝜈 𝑥 superscript 1 2 𝑥 2 𝜈 1 superscript subscript 𝑘 0 1 Euler-Gamma 𝜈 𝑘 1 Euler-Gamma 𝜈 2 𝑘 2 superscript 1 4 superscript 𝑥 2 2 𝑘 𝑘 {\displaystyle{\displaystyle\operatorname{ber}_{\nu}x\operatorname{bei}_{\nu}'% x-\operatorname{ber}_{\nu}'x\operatorname{bei}_{\nu}x=(\tfrac{1}{2}x)^{2\nu+1}% \sum_{k=0}^{\infty}\frac{1}{\Gamma\left(\nu+k+1\right)\Gamma\left(\nu+2k+2% \right)}\frac{(\frac{1}{4}x^{2})^{2k}}{k!},}}
    0 references
    DLMF id
    DLMF:10.65.E7
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
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    Kelvin function
    test
    bei ν ⁡ ( x ) Kelvin-bei 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{bei}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C10.S61.E1.m3afdec
    0 references
    Kelvin function
    test
    ber ν ⁡ ( x ) Kelvin-ber 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{ber}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C10.S61.E1.m2afdec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5afdec
    0 references
    Q11428
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1edec
    0 references
     
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