DLMF:13.18.E15 (Q4584): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11559 / rank
 
Normal rank
Property / Symbols used: Q11559 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11559 / qualifier
 
xml-id: C13.S1.XMD2.m1adec
Property / Symbols used
 
Property / Symbols used: Q11557 / rank
 
Normal rank
Property / Symbols used: Q11557 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11557 / qualifier
 
xml-id: C13.S1.XMD6.m1ndec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5aadec

Latest revision as of 15:13, 2 January 2020

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DLMF:13.18.E15
No description defined

    Statements

    test
    M 3 4 + n , 1 4 ⁡ ( z 2 ) = ( - 1 ) n ⁢ n ! ( 2 ⁢ n + 1 ) ! ⁢ e - 1 2 ⁢ z 2 ⁢ z 2 ⁢ H 2 ⁢ n + 1 ⁡ ( z ) , Whittaker-confluent-hypergeometric-M 3 4 𝑛 1 4 superscript 𝑧 2 superscript 1 𝑛 𝑛 2 𝑛 1 superscript 𝑒 1 2 superscript 𝑧 2 𝑧 2 Hermite-polynomial-H 2 𝑛 1 𝑧 {\displaystyle{\displaystyle M_{\frac{3}{4}+n,\frac{1}{4}}\left(z^{2}\right)=(% -1)^{n}\frac{n!}{(2n+1)!}\frac{e^{-\frac{1}{2}z^{2}}\sqrt{z}}{2}H_{2n+1}\left(% z\right),}}
    0 references
    DLMF id
    DLMF:13.18.E15
    0 references
    Symbols used
    Q10922
    test
    H n ⁡ ( x ) Hermite-polynomial-H 𝑛 𝑥 {\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r13.m2aadec
    0 references
    Whittaker confluent hypergeometric function
    test
    M κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E2.m2aidec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2agdec
    0 references
    Q11559
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1adec
    0 references
    Q11557
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1ndec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
     
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