DLMF:13.6.E15 (Q4402)

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DLMF:13.6.E15
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    Statements

    test
    M ⁡ ( 1 2 ⁢ a + 3 4 , 3 2 , 1 2 ⁢ z 2 ) = 2 1 2 ⁢ a - 5 4 ⁢ Γ ⁡ ( 1 2 ⁢ a + 1 4 ) ⁢ e 1 4 ⁢ z 2 z ⁢ π ⁢ ( U ⁡ ( a , - z ) - U ⁡ ( a , z ) ) . Kummer-confluent-hypergeometric-M 1 2 𝑎 3 4 3 2 1 2 superscript 𝑧 2 superscript 2 1 2 𝑎 5 4 Euler-Gamma 1 2 𝑎 1 4 superscript 𝑒 1 4 superscript 𝑧 2 𝑧 𝜋 parabolic-U 𝑎 𝑧 parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle M\left(\tfrac{1}{2}a+\tfrac{3}{4},\tfrac{3}{2},% \tfrac{1}{2}z^{2}\right)=\frac{2^{\frac{1}{2}a-\frac{5}{4}}\Gamma\left(\tfrac{% 1}{2}a+\tfrac{1}{4}\right)e^{\frac{1}{4}z^{2}}}{z\sqrt{\pi}}\*\left(U\left(a,-% z\right)-U\left(a,z\right)\right).}}
    0 references
    DLMF id
    DLMF:13.6.E15
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
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    $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function
    test
    M ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E2.m2agdec
    0 references
     
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