DLMF:2.5.E35 (Q811): Difference between revisions

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imported>Admin
 
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Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
test:

ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1aedec
Property / Symbols used
 
Property / Symbols used: Q10960 / rank
 
Normal rank
Property / Symbols used: Q10960 / qualifier
 
test:

res residue {\displaystyle{\displaystyle\Residue}}

\Residue
Property / Symbols used: Q10960 / qualifier
 
xml-id: C1.S10.SS3.p5.m4abdec
Property / Symbols used
 
Property / Symbols used: Q11010 / rank
 
Normal rank
Property / Symbols used: Q11010 / qualifier
 
test:

G j ⁢ k ⁢ ( z ) subscript 𝐺 𝑗 𝑘 𝑧 {\displaystyle{\displaystyle G_{jk}(z)}}

G_{jk}(z)
Property / Symbols used: Q11010 / qualifier
 
xml-id: C2.S5.XMD21.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11011 / rank
 
Normal rank
Property / Symbols used: Q11011 / qualifier
 
test:

p j ⁢ k subscript 𝑝 𝑗 𝑘 {\displaystyle{\displaystyle p_{jk}}}

p_{jk}
Property / Symbols used: Q11011 / qualifier
 
xml-id: C2.S5.XMD22.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11012 / rank
 
Normal rank
Property / Symbols used: Q11012 / qualifier
 
test:

q j ⁢ k > p j ⁢ k subscript 𝑞 𝑗 𝑘 subscript 𝑝 𝑗 𝑘 {\displaystyle{\displaystyle q_{jk}>p_{jk}}}

q_{jk}>p_{jk}
Property / Symbols used: Q11012 / qualifier
 
xml-id: C2.S5.XMD23.m1adec
Property / Symbols used
 
Property / Symbols used: Q11013 / rank
 
Normal rank
Property / Symbols used: Q11013 / qualifier
 
test:

E j ⁢ k ⁢ ( x ) subscript 𝐸 𝑗 𝑘 𝑥 {\displaystyle{\displaystyle E_{jk}(x)}}

E_{jk}(x)
Property / Symbols used: Q11013 / qualifier
 
xml-id: C2.S5.XMD24.m1dec
Property / Symbols used
 
Property / Symbols used: Q10994 / rank
 
Normal rank
Property / Symbols used: Q10994 / qualifier
 
test:

I ⁢ ( x ) 𝐼 𝑥 {\displaystyle{\displaystyle I(x)}}

I(x)
Property / Symbols used: Q10994 / qualifier
 
xml-id: C2.S5.XMD5.m1kdec

Latest revision as of 16:06, 1 January 2020

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DLMF:2.5.E35
No description defined

    Statements

    test
    I j ⁢ k ⁢ ( x ) = ∑ p j ⁢ k < ℜ ⁡ z < q j ⁢ k res ⁡ [ - x - z ⁢ G j ⁢ k ⁢ ( z ) ] + E j ⁢ k ⁢ ( x ) , subscript 𝐼 𝑗 𝑘 𝑥 subscript subscript 𝑝 𝑗 𝑘 𝑧 subscript 𝑞 𝑗 𝑘 residue delimited-[] superscript 𝑥 𝑧 subscript 𝐺 𝑗 𝑘 𝑧 subscript 𝐸 𝑗 𝑘 𝑥 {\displaystyle{\displaystyle I_{jk}(x)=\sum_{p_{jk}<\Re z<q_{jk}}\Residue\left% [-x^{-z}G_{jk}(z)\right]+E_{jk}(x),}}
    0 references
    DLMF id
    DLMF:2.5.E35
    0 references
    Symbols used
    Q10811
    test
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1aedec
    0 references
    Q10960
    test
    res residue {\displaystyle{\displaystyle\Residue}}
    xml-id
    C1.S10.SS3.p5.m4abdec
    0 references
    Q11010
    test
    G j ⁢ k ⁢ ( z ) subscript 𝐺 𝑗 𝑘 𝑧 {\displaystyle{\displaystyle G_{jk}(z)}}
    xml-id
    C2.S5.XMD21.m1cdec
    0 references
    Q11011
    test
    p j ⁢ k subscript 𝑝 𝑗 𝑘 {\displaystyle{\displaystyle p_{jk}}}
    xml-id
    C2.S5.XMD22.m1bdec
    0 references
    Q11012
    test
    q j ⁢ k > p j ⁢ k subscript 𝑞 𝑗 𝑘 subscript 𝑝 𝑗 𝑘 {\displaystyle{\displaystyle q_{jk}>p_{jk}}}
    xml-id
    C2.S5.XMD23.m1adec
    0 references
    Q11013
    test
    E j ⁢ k ⁢ ( x ) subscript 𝐸 𝑗 𝑘 𝑥 {\displaystyle{\displaystyle E_{jk}(x)}}
    xml-id
    C2.S5.XMD24.m1dec
    0 references
    Q10994
    test
    I ⁢ ( x ) 𝐼 𝑥 {\displaystyle{\displaystyle I(x)}}
    xml-id
    C2.S5.XMD5.m1kdec
    0 references
     
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