DLMF:28.28.E34 (Q8461): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: DLMF:28.28.E27 / rank
 
Normal rank
Property / Symbols used: DLMF:28.28.E27 / qualifier
 
Defining formula:

α ν , m ( s ) subscript superscript 𝛼 𝑠 𝜈 𝑚 {\displaystyle{\displaystyle\alpha^{(s)}_{\nu,m}}}

\alpha^{(s)}_{\nu,m}
Property / Symbols used: DLMF:28.28.E27 / qualifier
 
xml-id: C28.S28.XMD7.m1fdec

Latest revision as of 15:28, 2 January 2020

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DLMF:28.28.E34
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    Statements

    1 π 2 0 2 π me ν ( t , h 2 ) me - ν - 2 m - 1 ( t , h 2 ) sin t d t = ( - 1 ) m + 1 i h α ν , m ( 0 ) D 1 ( ν , ν + 2 m + 1 , 0 ) , 1 superscript 𝜋 2 superscript subscript principal-value-integral 0 2 𝜋 diffop Mathieu-me 𝜈 1 𝑡 superscript 2 Mathieu-me 𝜈 2 𝑚 1 𝑡 superscript 2 𝑡 𝑡 superscript 1 𝑚 1 imaginary-unit subscript superscript 𝛼 0 𝜈 𝑚 Mathieu-D 1 𝜈 𝜈 2 𝑚 1 0 {\displaystyle{\displaystyle\dfrac{1}{\pi^{2}}\pvint_{0}^{2\pi}\dfrac{\mathrm{% me}_{\nu}'\left(t,h^{2}\right)\mathrm{me}_{-\nu-2m-1}\left(t,h^{2}\right)}{% \sin t}\mathrm{d}t=(-1)^{m+1}\mathrm{i}h\alpha^{(0)}_{\nu,m}\mathrm{D}_{1}% \left(\nu,\nu+2m+1,0\right),}}
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    DLMF:28.28.E34
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    D j ( ν , μ , z ) Mathieu-D 𝑗 𝜈 𝜇 𝑧 {\displaystyle{\displaystyle\mathrm{D}_{\NVar{j}}\left(\NVar{\nu},\NVar{\mu},% \NVar{z}\right)}}
    C28.S28.E24.m1ajdec
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    me n ( z , q ) Mathieu-me 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{me}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    C28.S12.SS2.p2.m2amdec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aacdec
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    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1aaadec
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    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2awdec
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    a b superscript subscript principal-value-integral 𝑎 𝑏 {\displaystyle{\displaystyle\pvint_{\NVar{a}}^{\NVar{b}}}}
    C1.S4.E24.m2adec
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    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2akdec
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    m 𝑚 {\displaystyle{\displaystyle m}}
    C28.S1.XMD1.m1odec
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    h {\displaystyle{\displaystyle h}}
    C28.S1.XMD11.m1acdec
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    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C28.S1.XMD7.m1pdec
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    α ν , m ( s ) subscript superscript 𝛼 𝑠 𝜈 𝑚 {\displaystyle{\displaystyle\alpha^{(s)}_{\nu,m}}}
    C28.S28.XMD7.m1fdec
    0 references