DLMF:11.4.E19 (Q3951): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Struve function / rank
 
Normal rank
Property / Symbols used: Struve function / qualifier
 
test:

𝐇 ν ⁡ ( z ) Struve-H 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}

\StruveH{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Struve function / qualifier
 
xml-id: C11.S2.E1.m2aidec
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
 
test:

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.m2andec
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.m5acdec
Property / Symbols used
 
Property / Symbols used: Q11491 / rank
 
Normal rank
Property / Symbols used: Q11491 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11491 / qualifier
 
xml-id: C11.S1.XMD2.m1qdec
Property / Symbols used
 
Property / Symbols used: Q11492 / rank
 
Normal rank
Property / Symbols used: Q11492 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11492 / qualifier
 
xml-id: C11.S1.XMD3.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11497 / rank
 
Normal rank
Property / Symbols used: Q11497 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11497 / qualifier
 
xml-id: C11.S1.XMD5.m1adec

Latest revision as of 13:41, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:11.4.E19
No description defined

    Statements

    test
    𝐇 ν ⁡ ( z ) = ( z 2 ⁢ π ) 1 / 2 ⁢ ∑ k = 0 ∞ ( 1 2 ⁢ z ) k k ! ⁢ ( k + 1 2 ) ⁢ J k + ν + 1 2 ⁡ ( z ) , Struve-H 𝜈 𝑧 superscript 𝑧 2 𝜋 1 2 superscript subscript 𝑘 0 superscript 1 2 𝑧 𝑘 𝑘 𝑘 1 2 Bessel-J 𝑘 𝜈 1 2 𝑧 {\displaystyle{\displaystyle\mathbf{H}_{\nu}\left(z\right)=\left(\frac{z}{2\pi% }\right)^{1/2}\sum_{k=0}^{\infty}\frac{(\tfrac{1}{2}z)^{k}}{k!(k+\tfrac{1}{2})% }J_{k+\nu+\frac{1}{2}}\left(z\right),}}
    0 references
    DLMF id
    DLMF:11.4.E19
    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
    Struve function
    test
    𝐇 ν ⁡ ( z ) Struve-H 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S2.E1.m2aidec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2andec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5acdec
    0 references
    Q11491
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1qdec
    0 references
    Q11492
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1fdec
    0 references
    Q11497
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C11.S1.XMD5.m1adec
    0 references
     
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