DLMF:11.2.E2 (Q3917): 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.m2aadec
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: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2adec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2adec
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.m1adec
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.m1adec
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.m1adec

Latest revision as of 13:35, 2 January 2020

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DLMF:11.2.E2
No description defined

    Statements

    test
    𝐋 ν ⁡ ( z ) = - i ⁢ e - 1 2 ⁢ π ⁢ i ⁢ ν ⁢ 𝐇 ν ⁡ ( i ⁢ z ) = ( 1 2 ⁢ z ) ν + 1 ⁢ ∑ n = 0 ∞ ( 1 2 ⁢ z ) 2 ⁢ n Γ ⁡ ( n + 3 2 ) ⁢ Γ ⁡ ( n + ν + 3 2 ) . modified-Struve-L 𝜈 𝑧 𝑖 superscript 𝑒 1 2 𝜋 𝑖 𝜈 Struve-H 𝜈 𝑖 𝑧 superscript 1 2 𝑧 𝜈 1 superscript subscript 𝑛 0 superscript 1 2 𝑧 2 𝑛 Euler-Gamma 𝑛 3 2 Euler-Gamma 𝑛 𝜈 3 2 {\displaystyle{\displaystyle\mathbf{L}_{\nu}\left(z\right)=-ie^{-\frac{1}{2}% \pi i\nu}\mathbf{H}_{\nu}\left(iz\right)=(\tfrac{1}{2}z)^{\nu+1}\sum_{n=0}^{% \infty}\frac{(\tfrac{1}{2}z)^{2n}}{\Gamma\left(n+\tfrac{3}{2}\right)\Gamma% \left(n+\nu+\tfrac{3}{2}\right)}.}}
    0 references
    DLMF id
    DLMF:11.2.E2
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    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.m2aadec
    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
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q11491
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1adec
    0 references
    Q11492
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1adec
    0 references
    Q11493
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C11.S1.XMD4.m1adec
    0 references
     
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