DLMF:8.21.E17 (Q2739): Difference between revisions

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Property / constraint
 

a ≠ 0 , - 2 , - 4 , … 𝑎 0 2 4 … {\displaystyle{\displaystyle a\neq 0,-2,-4,\dots}}

a\neq 0,-2,-4,\dots
Property / constraint: a ≠ 0 , - 2 , - 4 , … 𝑎 0 2 4 … {\displaystyle{\displaystyle a\neq 0,-2,-4,\dots}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q10759 / rank
 
Normal rank
Property / Symbols used: Q10759 / qualifier
 
test:

( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

\Pochhammersym{\NVar{a}}{\NVar{n}}
Property / Symbols used: Q10759 / qualifier
 
xml-id: C5.S2.SS3.m1aadec
Property / Symbols used
 
Property / Symbols used: generalized cosine integral / rank
 
Normal rank
Property / Symbols used: generalized cosine integral / qualifier
 
test:

Ci ⁡ ( a , z ) generalized-cosine-integral-Ci 𝑎 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(\NVar{a},\NVar{z}\right)}}

\gencosint@{\NVar{a}}{\NVar{z}}
Property / Symbols used: generalized cosine integral / qualifier
 
xml-id: C8.S21.E2.m2aedec
Property / Symbols used
 
Property / Symbols used: spherical Bessel function of the first kind / rank
 
Normal rank
Property / Symbols used: spherical Bessel function of the first kind / qualifier
 
test:

𝗃 n ⁡ ( z ) spherical-Bessel-J 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)}}

\sphBesselJ{\NVar{n}}@{\NVar{z}}
Property / Symbols used: spherical Bessel function of the first kind / qualifier
 
xml-id: C10.S47.E3.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11323 / rank
 
Normal rank
Property / Symbols used: Q11323 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11323 / qualifier
 
xml-id: C8.S1.XMD2.m1mdec
Property / Symbols used
 
Property / Symbols used: Q11324 / rank
 
Normal rank
Property / Symbols used: Q11324 / qualifier
 
test:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11324 / qualifier
 
xml-id: C8.S1.XMD3.m1ndec
Property / Symbols used
 
Property / Symbols used: Q11330 / rank
 
Normal rank
Property / Symbols used: Q11330 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11330 / qualifier
 
xml-id: C8.S1.XMD5.m1cdec

Latest revision as of 13:18, 2 January 2020

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DLMF:8.21.E17
No description defined

    Statements

    test
    Ci ⁡ ( a , z ) = z a ⁢ ∑ k = 0 ∞ ( 2 ⁢ k + 1 2 ) ⁢ ( 1 2 - 1 2 ⁢ a ) k ( 1 2 ⁢ a ) k + 1 ⁢ 𝗃 2 ⁢ k ⁡ ( z ) , generalized-cosine-integral-Ci 𝑎 𝑧 superscript 𝑧 𝑎 superscript subscript 𝑘 0 2 𝑘 1 2 Pochhammer 1 2 1 2 𝑎 𝑘 Pochhammer 1 2 𝑎 𝑘 1 spherical-Bessel-J 2 𝑘 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(a,z\right)=z^{a}\sum_{k=0}^{% \infty}\frac{\left(2k+\frac{1}{2}\right){\left(\frac{1}{2}-\frac{1}{2}a\right)% _{k}}}{{\left(\frac{1}{2}a\right)_{k+1}}}\mathsf{j}_{2k}\left(z\right),}}
    0 references
    DLMF id
    DLMF:8.21.E17
    0 references
    constraint
    a ≠ 0 , - 2 , - 4 , … 𝑎 0 2 4 … {\displaystyle{\displaystyle a\neq 0,-2,-4,\dots}}
    0 references
    Symbols used
    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1aadec
    0 references
    generalized cosine integral
    test
    Ci ⁡ ( a , z ) generalized-cosine-integral-Ci 𝑎 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S21.E2.m2aedec
    0 references
    spherical Bessel function of the first kind
    test
    𝗃 n ⁡ ( z ) spherical-Bessel-J 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E3.m2aadec
    0 references
    Q11323
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1mdec
    0 references
    Q11324
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1ndec
    0 references
    Q11330
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C8.S1.XMD5.m1cdec
    0 references
     
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