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DLMF:6.11.E3 - MaRDI portal

DLMF:6.11.E3 (Q2986)

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DLMF:6.11.E3
No description defined

    Statements

    DLMF defining formula
    g ⁡ ( z ) + i ⁢ f ⁡ ( z ) = U ⁡ ( 1 , 1 , - i ⁢ z ) . sine-cosine-integral-g 𝑧 𝑖 sine-cosine-integral-f 𝑧 Kummer-confluent-hypergeometric-U 1 1 𝑖 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(z\right)+i\mathrm{f}\left(z\right)% =U\left(1,1,-iz\right).}}
    0 references
    Symbols used
    Kummer confluent hypergeometric function
    DLMF defining formula
    U ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E6.m2aadec
    0 references
    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    auxiliary function for sine and cosine integrals
    DLMF defining formula
    f ⁡ ( z ) sine-cosine-integral-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E17.m2adec
    0 references
    auxiliary function for sine and cosine integrals
    DLMF defining formula
    g ⁡ ( z ) sine-cosine-integral-g 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E18.m2adec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C6.S1.XMD2.m1bdec
    0 references

    Identifiers

     
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