DLMF:6.10.E8 (Q2285): Difference between revisions

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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.m1cdec
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.m1ddec

Latest revision as of 01:31, 2 January 2020

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DLMF:6.10.E8
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    Statements

    Defining formula
    Ein ⁡ ( z ) = z ⁢ e - z / 2 ⁢ ( 𝗂 0 ( 1 ) ⁡ ( 1 2 ⁢ z ) + ∑ n = 1 ∞ 2 ⁢ n + 1 n ⁢ ( n + 1 ) ⁢ 𝗂 n ( 1 ) ⁡ ( 1 2 ⁢ z ) ) . complementary-exponential-integral 𝑧 𝑧 superscript 𝑒 𝑧 2 spherical-Bessel-I-1 0 1 2 𝑧 superscript subscript 𝑛 1 2 𝑛 1 𝑛 𝑛 1 spherical-Bessel-I-1 𝑛 1 2 𝑧 {\displaystyle{\displaystyle\mathrm{Ein}\left(z\right)=ze^{-z/2}\left({\mathsf% {i}^{(1)}_{0}}\left(\tfrac{1}{2}z\right)+\sum_{n=1}^{\infty}\dfrac{2n+1}{n(n+1% )}{\mathsf{i}^{(1)}_{n}}\left(\tfrac{1}{2}z\right)\right).}}
    0 references
    DLMF id
    DLMF:6.10.E8
    0 references
    Symbols used
    complementary exponential integral
    Defining formula
    Ein ⁡ ( z ) complementary-exponential-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Ein}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E3.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    modified spherical Bessel function
    Defining formula
    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.m2aadec
    0 references
    Q11305
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C6.S1.XMD2.m1cdec
    0 references
    Q11308
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C6.S1.XMD3.m1ddec
    0 references
     
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