DLMF:18.23.E6 (Q5907)

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DLMF:18.23.E6
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    Statements

    test
    F 1 1 ⁡ ( a + i ⁢ x 2 ⁢ ℜ ⁡ a ; - i ⁢ z ) ⁢ F 1 1 ⁡ ( b ¯ - i ⁢ x 2 ⁢ ℜ ⁡ b ; i ⁢ z ) = ∑ n = 0 ∞ p n ⁡ ( x ; a , b , a ¯ , b ¯ ) ( 2 ⁢ ℜ ⁡ a ) n ⁢ ( 2 ⁢ ℜ ⁡ b ) n ⁢ z n . Kummer-confluent-hypergeometric-M-as-1F1 𝑎 imaginary-unit 𝑥 2 𝑎 imaginary-unit 𝑧 Kummer-confluent-hypergeometric-M-as-1F1 𝑏 imaginary-unit 𝑥 2 𝑏 imaginary-unit 𝑧 superscript subscript 𝑛 0 continuous-Hahn-polynomial-p 𝑛 𝑥 𝑎 𝑏 𝑎 𝑏 Pochhammer 2 𝑎 𝑛 Pochhammer 2 𝑏 𝑛 superscript 𝑧 𝑛 {\displaystyle{\displaystyle{{}_{1}F_{1}}\left({a+\mathrm{i}x\atop 2\Re a};-% \mathrm{i}z\right){{}_{1}F_{1}}\left({\overline{b}-\mathrm{i}x\atop 2\Re b};% \mathrm{i}z\right)=\sum_{n=0}^{\infty}\frac{p_{n}\left(x;a,b,\overline{a},% \overline{b}\right)}{{\left(2\Re a\right)_{n}}{\left(2\Re b\right)_{n}}}z^{n}.}}
    0 references
    DLMF id
    DLMF:18.23.E6
    0 references
    Symbols used
    Q11384
    test
    F 1 1 ⁡ ( a ; b ; z ) Kummer-confluent-hypergeometric-M-as-1F1 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle{{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}% \right)}}
    xml-id
    C16.S2.m7aadec
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    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1acdec
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    complex conjugate
    test
    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    xml-id
    C1.S9.E11.m2adec
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    Q11763
    test
    p n ⁡ ( x ; a , b , a ¯ , missing ) continuous-Hahn-polynomial-p 𝑛 𝑥 𝑎 𝑏 𝑎 missing {\displaystyle{\displaystyle p_{\NVar{n}}\left(\NVar{x};\NVar{a},\NVar{b},% \NVar{\overline{a}},\NVar{missing}\right)\)\@add@PDF@RDFa@triples\end{document}}}
    xml-id
    C18.S19.Px2.p1.m4adec
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    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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    Q10811
    test
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
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    Q11750
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C18.S1.XMD2.m1edec
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    Q11726
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1edec
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    Q11727
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1edec
    0 references
     
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