DLMF:10.21.E16 (Q3300): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older edit
imported>Admin
imported>Admin
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q11458 / rank
 
Normal rank
Property / Symbols used: Q11458 / qualifier
 
test:

j ν , m ′ zero-derivative-Bessel-J 𝜈 𝑚 {\displaystyle{\displaystyle{j^{\prime}_{\NVar{\nu},\NVar{m}}}}}

\zderivBesselj{\NVar{\nu}}{\NVar{m}}
Property / Symbols used: Q11458 / qualifier
 
xml-id: C10.S21.SS1.p2.m15aedec
Property / Symbols used
 
Property / Symbols used: Q11428 / rank
 
Normal rank
Property / Symbols used: Q11428 / qualifier
 
test:

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
 
test:

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
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1ndec

Latest revision as of 14:41, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:10.21.E16
No description defined

    Statements

    test
    J ν ′ ⁡ ( z ) = ( 1 2 ⁢ z ) ν - 1 2 ⁢ Γ ⁡ ( ν ) ⁢ ∏ k = 1 ∞ ( 1 - z 2 j ν , k ′ 2 ) , diffop Bessel-J 𝜈 1 𝑧 superscript 1 2 𝑧 𝜈 1 2 Euler-Gamma 𝜈 superscript subscript product 𝑘 1 1 superscript 𝑧 2 zero-derivative-Bessel-J 𝜈 𝑘 2 {\displaystyle{\displaystyle J_{\nu}'\left(z\right)=\frac{(\tfrac{1}{2}z)^{\nu% -1}}{2\Gamma\left(\nu\right)}\prod_{k=1}^{\infty}\left(1-\frac{z^{2}}{{{j^{% \prime}_{\nu,k}}^{\mspace{-16.0mu }2}}}\right),}}
    0 references
    DLMF id
    DLMF:10.21.E16
    0 references
    constraint
    ν > 0 𝜈 0 {\displaystyle{\displaystyle\nu>0}}
    0 references
    Symbols used
    Bessel function of the first kind
    test
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2abdec
    0 references
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    Q11458
    test
    j ν , m ′ zero-derivative-Bessel-J 𝜈 𝑚 {\displaystyle{\displaystyle{j^{\prime}_{\NVar{\nu},\NVar{m}}}}}
    xml-id
    C10.S21.SS1.p2.m15aedec
    0 references
    Q11428
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1adec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1bdec
    0 references
    Q11427
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1ndec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q3300&oldid=17275"