DLMF:6.11.E3 (Q2288)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:6.11.E3
No description defined

    Statements

    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
    DLMF id
    DLMF:6.11.E3
    0 references
    Symbols used
    Kummer confluent hypergeometric function
    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
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    auxiliary function for sine and cosine integrals
    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
    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
    Q11305
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C6.S1.XMD2.m1bdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q2288&oldid=32260"