DLMF:35.8.E2 (Q10516)

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DLMF:35.8.E2
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    Statements

    DLMF defining formula
    F 0 0 ⁡ ( - - ; 𝐓 ) = etr ⁡ ( 𝐓 ) , Gauss-hypergeometric-of-matrix-pFq 0 0 𝐓 exponential-trace 𝐓 {\displaystyle{\displaystyle{{}_{0}F_{0}}\left({-\atop-};\mathbf{T}\right)=% \mathrm{etr}\left(\mathbf{T}\right),}}
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    constraint
    𝐓 ∈ 𝓢 𝐓 𝓢 {\displaystyle{\displaystyle\mathbf{T}\in\boldsymbol{\mathcal{S}}}}
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    Symbols used
    generalized hypergeometric function of matrix argument
    DLMF defining formula
    F q p ⁡ ( a 1 , … , a p ; b 1 , … , b q ; 𝐓 ) Gauss-hypergeometric-of-matrix-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝐓 {\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{\mathbf{T}}\right)}}
    xml-id
    C35.S8.E1.m2aadec
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    Q10758
    DLMF defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2adec
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    Q12721
    DLMF defining formula
    etr ⁡ ( 𝐗 ) exponential-trace 𝐗 {\displaystyle{\displaystyle\mathrm{etr}\left(\NVar{\mathbf{X}}\right)}}
    xml-id
    C35.S1.p3.t1.r10.m3adec
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    space of real symmetric matrices
    DLMF defining formula
    𝐓 𝐓 {\displaystyle{\displaystyle\mathbf{T}}}
    xml-id
    C35.S1.XMD11.m1adec
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    matrix of zeros
    DLMF defining formula
    𝓢 𝓢 {\displaystyle{\displaystyle\boldsymbol{\mathcal{S}}}}
    xml-id
    C35.S1.XMD9.m1dec
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