DLMF:6.10.E6 (Q2283): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11306 / rank
 
Normal rank
Property / Symbols used: Q11306 / qualifier
 
test:

Ei ⁡ ( x ) exponential-integral-Ei 𝑥 {\displaystyle{\displaystyle\mathrm{Ei}\left(\NVar{x}\right)}}

\expintEi@{\NVar{x}}
Property / Symbols used: Q11306 / qualifier
 
xml-id: C6.S2.SS1.p3.m2adec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2adec
Property / Symbols used
 
Property / Symbols used: modified spherical Bessel function / rank
 
Normal rank
Property / Symbols used: modified spherical Bessel function / qualifier
 
test:

𝗂 n ( 1 ) ⁡ ( z ) spherical-Bessel-I-1 𝑛 𝑧 {\displaystyle{\displaystyle{\mathsf{i}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)}}

\modsphBesseli{1}{\NVar{n}}@{\NVar{z}}
Property / Symbols used: modified spherical Bessel function / qualifier
 
xml-id: C10.S47.E7.m2adec
Property / Symbols used
 
Property / Symbols used: Q11307 / rank
 
Normal rank
Property / Symbols used: Q11307 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11307 / qualifier
 
xml-id: C6.S1.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: Q11308 / rank
 
Normal rank
Property / Symbols used: Q11308 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11308 / qualifier
 
xml-id: C6.S1.XMD3.m1bdec
Property / Symbols used
 
Property / Symbols used: coefficients (locally) / rank
 
Normal rank
Property / Symbols used: coefficients (locally) / qualifier
 
test:

a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}

a_{n}
Property / Symbols used: coefficients (locally) / qualifier
 
xml-id: C6.S10.XMD1.m1adec

Latest revision as of 01:31, 2 January 2020

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DLMF:6.10.E6
No description defined

    Statements

    test
    Ei ⁡ ( x ) = γ + ln ⁡ | x | + ∑ n = 0 ∞ ( - 1 ) n ⁢ ( x - a n ) ⁢ ( 𝗂 n ( 1 ) ⁡ ( 1 2 ⁢ x ) ) 2 , exponential-integral-Ei 𝑥 𝑥 superscript subscript 𝑛 0 superscript 1 𝑛 𝑥 subscript 𝑎 𝑛 superscript spherical-Bessel-I-1 𝑛 1 2 𝑥 2 {\displaystyle{\displaystyle\mathrm{Ei}\left(x\right)=\gamma+\ln\left|x\right|% +\sum_{n=0}^{\infty}(-1)^{n}(x-a_{n})\left({\mathsf{i}^{(1)}_{n}}\left(\tfrac{% 1}{2}x\right)\right)^{2},}}
    0 references
    DLMF id
    DLMF:6.10.E6
    0 references
    constraint
    x ≠ 0 𝑥 0 {\displaystyle{\displaystyle x\neq 0}}
    0 references
    Symbols used
    Euler’s constant
    test
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2adec
    0 references
    Q11306
    test
    Ei ⁡ ( x ) exponential-integral-Ei 𝑥 {\displaystyle{\displaystyle\mathrm{Ei}\left(\NVar{x}\right)}}
    xml-id
    C6.S2.SS1.p3.m2adec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    modified spherical Bessel function
    test
    𝗂 n ( 1 ) ⁡ ( z ) spherical-Bessel-I-1 𝑛 𝑧 {\displaystyle{\displaystyle{\mathsf{i}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E7.m2adec
    0 references
    Q11307
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C6.S1.XMD1.m1dec
    0 references
    Q11308
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C6.S1.XMD3.m1bdec
    0 references
    coefficients (locally)
    test
    a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}
    xml-id
    C6.S10.XMD1.m1adec
    0 references
     
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