DLMF:13.8.E7 (Q4432)

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DLMF:13.8.E7
No description defined

    Statements

    Defining formula
    U ⁡ ( a , b , b ) = π ⁢ ( 2 ⁢ b ) - 1 2 ⁢ a ⁢ ( 1 Γ ⁡ ( 1 2 ⁢ ( a + 1 ) ) - ( a + 1 ) ⁢ 8 / b 3 ⁢ Γ ⁡ ( 1 2 ⁢ a ) + O ⁡ ( 1 b ) ) . Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑏 𝜋 superscript 2 𝑏 1 2 𝑎 1 Euler-Gamma 1 2 𝑎 1 𝑎 1 8 𝑏 3 Euler-Gamma 1 2 𝑎 Big-O 1 𝑏 {\displaystyle{\displaystyle U\left(a,b,b\right)=\sqrt{\pi}\left(2b\right)^{-% \frac{1}{2}a}\left(\frac{1}{\Gamma\left(\frac{1}{2}(a+1)\right)}-\frac{(a+1)% \sqrt{8/b}}{3\Gamma\left(\frac{1}{2}a\right)}+O\left(\frac{1}{b}\right)\right)% .}}
    0 references
    DLMF id
    DLMF:13.8.E7
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2abdec
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    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
    0 references
    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
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
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