DLMF:6.5.E3 (Q2243): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2abdec

Revision as of 01:24, 2 January 2020

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DLMF:6.5.E3
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    Statements

    test
    1 2 ⁢ ( Ei ⁡ ( x ) + E 1 ⁡ ( x ) ) = Shi ⁡ ( x ) = - i ⁢ Si ⁡ ( i ⁢ x ) , 1 2 exponential-integral-Ei 𝑥 exponential-integral 𝑥 hyperbolic-sine-integral 𝑥 𝑖 sine-integral 𝑖 𝑥 {\displaystyle{\displaystyle\tfrac{1}{2}(\mathrm{Ei}\left(x\right)+E_{1}\left(% x\right))=\mathrm{Shi}\left(x\right)=-i\mathrm{Si}\left(ix\right),}}
    0 references
    DLMF id
    DLMF:6.5.E3
    0 references
    Symbols used
    exponential integral
    test
    E 1 ⁡ ( z ) exponential-integral 𝑧 {\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E1.m2abdec
    0 references
    Q11306
    test
    Ei ⁡ ( x ) exponential-integral-Ei 𝑥 {\displaystyle{\displaystyle\mathrm{Ei}\left(\NVar{x}\right)}}
    xml-id
    C6.S2.SS1.p3.m2abdec
    0 references
    hyperbolic sine integral
    test
    Shi ⁡ ( z ) hyperbolic-sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Shi}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E15.m2adec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
     
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