DLMF:11.10.E22 (Q4041): 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.m2adec
Property / Symbols used
 
Property / Symbols used: Weber function / rank
 
Normal rank
Property / Symbols used: Weber function / qualifier
 
test:

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

\WeberE{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Weber function / qualifier
 
xml-id: C11.S10.E2.m2amdec
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.m2aqdec
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.m1udec
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
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.m1bdec

Latest revision as of 13:57, 2 January 2020

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English
DLMF:11.10.E22
No description defined

    Statements

    test
    𝐄 n ⁡ ( z ) = - 𝐇 n ⁡ ( z ) + 1 π ⁢ ∑ k = 0 m 1 Γ ⁡ ( k + 1 2 ) Γ ⁡ ( n + 1 2 - k ) ⁢ ( 1 2 ⁢ z ) n - 2 ⁢ k - 1 , Weber-E 𝑛 𝑧 Struve-H 𝑛 𝑧 1 𝜋 superscript subscript 𝑘 0 subscript 𝑚 1 Euler-Gamma 𝑘 1 2 Euler-Gamma 𝑛 1 2 𝑘 superscript 1 2 𝑧 𝑛 2 𝑘 1 {\displaystyle{\displaystyle\mathbf{E}_{n}\left(z\right)=-\mathbf{H}_{n}\left(% z\right)+\frac{1}{\pi}\sum_{k=0}^{m_{1}}\frac{\Gamma\left(k+\tfrac{1}{2}\right% )}{\Gamma\left(n\!+\!\tfrac{1}{2}\!-\!k\right)}(\tfrac{1}{2}z)^{n-2k-1},}}
    0 references
    DLMF id
    DLMF:11.10.E22
    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
    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.m2adec
    0 references
    Weber function
    test
    𝐄 ν ⁡ ( z ) Weber-E 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{E}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E2.m2amdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aqdec
    0 references
    Q11491
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1udec
    0 references
    Q11493
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C11.S1.XMD4.m1dec
    0 references
    Q11497
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C11.S1.XMD5.m1bdec
    0 references
     
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