DLMF:11.4.E1 (Q3933): 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:

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

\StruveK{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Struve function / qualifier
 
xml-id: C11.S2.E5.m2adec
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.m2adec
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.m5adec
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.m1dec
Property / Symbols used
 
Property / Symbols used: Q11493 / rank
 
Normal rank
Property / Symbols used: Q11493 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11493 / qualifier
 
xml-id: C11.S1.XMD4.m1dec

Latest revision as of 13:38, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:11.4.E1
No description defined

    Statements

    test
    𝐊 n + 1 2 ⁡ ( z ) = ( 2 π ⁢ z ) 1 2 ⁢ ∑ m = 0 n ( 2 ⁢ m ) ! ⁢  2 - 2 ⁢ m m ! ⁢ ( n - m ) ! ⁢ ( 1 2 ⁢ z ) n - 2 ⁢ m , associated-Struve-K 𝑛 1 2 𝑧 superscript 2 𝜋 𝑧 1 2 superscript subscript 𝑚 0 𝑛 2 𝑚 superscript  2 2 𝑚 𝑚 𝑛 𝑚 superscript 1 2 𝑧 𝑛 2 𝑚 {\displaystyle{\displaystyle\mathbf{K}_{n+\frac{1}{2}}\left(z\right)=\left(% \frac{2}{\pi z}\right)^{\frac{1}{2}}\sum_{m=0}^{n}\frac{(2m)!\,2^{-2m}}{m!\,(n% -m)!}\,(\tfrac{1}{2}z)^{n-2m},}}
    0 references
    DLMF id
    DLMF:11.4.E1
    0 references
    Symbols used
    Struve function
    test
    𝐊 ν ⁡ ( z ) associated-Struve-K 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{K}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S2.E5.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    Q11491
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1dec
    0 references
    Q11493
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C11.S1.XMD4.m1dec
    0 references
     
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