DLMF:6.12.E6 (Q2294): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: auxiliary function for sine and cosine integrals / rank
 
Normal rank
Property / Symbols used: auxiliary function for sine and cosine integrals / qualifier
 
Defining formula:

g ( z ) sine-cosine-integral-g 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(\NVar{z}\right)}}

\auxsincosintg@{\NVar{z}}
Property / Symbols used: auxiliary function for sine and cosine integrals / qualifier
 
xml-id: C6.S2.E18.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11305 / rank
 
Normal rank
Property / Symbols used: Q11305 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11305 / qualifier
 
xml-id: C6.S1.XMD2.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11308 / rank
 
Normal rank
Property / Symbols used: Q11308 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11308 / qualifier
 
xml-id: C6.S1.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: remainder term (locally) / rank
 
Normal rank
Property / Symbols used: remainder term (locally) / qualifier
 
Defining formula:

R n ( g ) ( z ) superscript subscript 𝑅 𝑛 sine-cosine-integral-g 𝑧 {\displaystyle{\displaystyle R_{n}^{(\mathrm{g})}(z)}}

R_{n}^{(\auxsincosintg)}(z)
Property / Symbols used: remainder term (locally) / qualifier
 
xml-id: C6.S12.XMD2.m1dec

Latest revision as of 01:32, 2 January 2020

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DLMF:6.12.E6
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    Statements

    g ( z ) = 1 z 2 m = 0 n - 1 ( - 1 ) m ( 2 m + 1 ) ! z 2 m + R n ( g ) ( z ) , sine-cosine-integral-g 𝑧 1 superscript 𝑧 2 superscript subscript 𝑚 0 𝑛 1 superscript 1 𝑚 2 𝑚 1 superscript 𝑧 2 𝑚 superscript subscript 𝑅 𝑛 sine-cosine-integral-g 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(z\right)=\frac{1}{z^{2}}\sum_{m=0}% ^{n-1}(-1)^{m}\frac{(2m+1)!}{z^{2m}}+R_{n}^{(\mathrm{g})}(z),}}
    0 references
    DLMF:6.12.E6
    0 references
    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5aedec
    0 references
    g ( z ) sine-cosine-integral-g 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(\NVar{z}\right)}}
    C6.S2.E18.m2aadec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C6.S1.XMD2.m1ddec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C6.S1.XMD3.m1adec
    0 references
    R n ( g ) ( z ) superscript subscript 𝑅 𝑛 sine-cosine-integral-g 𝑧 {\displaystyle{\displaystyle R_{n}^{(\mathrm{g})}(z)}}
    C6.S12.XMD2.m1dec
    0 references