DLMF:13.4.E8 (Q4371)

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DLMF:13.4.E8
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    Statements

    Defining formula
    U ⁡ ( a , b , z ) = z c - a ⁢ ∫ 0 ∞ e - z ⁢ t ⁢ t c - 1 ⁢ 𝐅 1 2 ⁡ ( a , a - b + 1 ; c ; - t ) ⁢ d t , Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 𝑧 𝑐 𝑎 superscript subscript 0 superscript 𝑒 𝑧 𝑡 superscript 𝑡 𝑐 1 hypergeometric-bold-pFq 2 1 𝑎 𝑎 𝑏 1 𝑐 𝑡 𝑡 {\displaystyle{\displaystyle U\left(a,b,z\right)=z^{c-a}\*\int_{0}^{\infty}e^{% -zt}t^{c-1}{{}_{2}{\mathbf{F}}_{1}}\left(a,a-b+1;c;-t\right)\mathrm{d}t,}}
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    DLMF id
    DLMF:13.4.E8
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    constraint
    | ph ⁡ z | < 1 2 ⁢ π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}{z}|<\frac{1}{2}\pi}}
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    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.m2addec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1agdec
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