DLMF:10.65.E8 (Q3841): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5agdec

Revision as of 14:23, 2 January 2020

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English
DLMF:10.65.E8
No description defined

    Statements

    test
    ber ν ⁡ x ⁢ ber ν ′ ⁡ x + bei ν ⁡ x ⁢ bei ν ′ ⁡ x = 1 2 ⁢ ( 1 2 ⁢ x ) 2 ⁢ ν - 1 ⁢ ∑ k = 0 ∞ 1 Γ ⁡ ( ν + k + 1 ) ⁢ Γ ⁡ ( ν + 2 ⁢ k ) ⁢ ( 1 4 ⁢ x 2 ) 2 ⁢ k k ! , Kelvin-ber 𝜈 𝑥 diffop Kelvin-ber 𝜈 1 𝑥 Kelvin-bei 𝜈 𝑥 diffop Kelvin-bei 𝜈 1 𝑥 1 2 superscript 1 2 𝑥 2 𝜈 1 superscript subscript 𝑘 0 1 Euler-Gamma 𝜈 𝑘 1 Euler-Gamma 𝜈 2 𝑘 superscript 1 4 superscript 𝑥 2 2 𝑘 𝑘 {\displaystyle{\displaystyle\operatorname{ber}_{\nu}x\operatorname{ber}_{\nu}'% x+\operatorname{bei}_{\nu}x\operatorname{bei}_{\nu}'x=\tfrac{1}{2}(\tfrac{1}{2% }x)^{2\nu-1}\sum_{k=0}^{\infty}\frac{1}{\Gamma\left(\nu+k+1\right)\Gamma\left(% \nu+2k\right)}\frac{(\frac{1}{4}x^{2})^{2k}}{k!},}}
    0 references
    DLMF id
    DLMF:10.65.E8
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
    0 references
    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.m3agdec
    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.m2agdec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5agdec
    0 references
     
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