DLMF:32.15.E1 (Q9493)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:32.15.E1
No description defined

    Statements

    Defining formula
    ∫ - ∞ ∞ exp ⁡ ( - 1 4 ⁢ ξ 4 - z ⁢ ξ 2 ) ⁢ p m ⁢ ( ξ ) ⁢ p n ⁢ ( ξ ) ⁢ d ξ = δ m , n , superscript subscript 1 4 superscript 𝜉 4 𝑧 superscript 𝜉 2 subscript 𝑝 𝑚 𝜉 subscript 𝑝 𝑛 𝜉 𝜉 Kronecker 𝑚 𝑛 {\displaystyle{\displaystyle\int_{-\infty}^{\infty}\exp\left(-\tfrac{1}{4}\xi^% {4}-z\xi^{2}\right)p_{m}(\xi)p_{n}(\xi)\mathrm{d}\xi=\delta_{m,n},}}
    0 references
    DLMF id
    DLMF:32.15.E1
    0 references
    Symbols used
    Q10768
    Defining formula
    δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}
    xml-id
    introduction.Sx4.p1.t1.r4.m5adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q12573
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C32.S1.XMD1.m1dec
    0 references
    Q12571
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C32.S1.XMD2.m1dec
    0 references
    Q12523
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C32.S1.XMD4.m1dec
    0 references
    Q12664
    Defining formula
    p n ⁢ ( ξ ) subscript 𝑝 𝑛 𝜉 {\displaystyle{\displaystyle p_{n}(\xi)}}
    xml-id
    C32.S15.XMD1.m1dec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q9493&oldid=45826"