DLMF:19.36.E13 (Q6740)

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DLMF:19.36.E13
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    Statements

    Defining formula
    2 ⁢ R G ⁡ ( t 0 2 , t 0 2 + θ ⁢ c 0 2 , t 0 2 + θ ⁢ a 0 2 ) = ( t 0 2 + θ ⁢ ∑ m = 0 ∞ 2 m - 1 ⁢ c m 2 ) ⁢ R C ⁡ ( T 2 + θ ⁢ M 2 , T 2 ) + h 0 + ∑ m = 1 ∞ 2 m ⁢ ( h m - h m - 1 ) . 2 Carlson-integral-RG superscript subscript 𝑡 0 2 superscript subscript 𝑡 0 2 𝜃 superscript subscript 𝑐 0 2 superscript subscript 𝑡 0 2 𝜃 superscript subscript 𝑎 0 2 superscript subscript 𝑡 0 2 𝜃 superscript subscript 𝑚 0 superscript 2 𝑚 1 superscript subscript 𝑐 𝑚 2 Carlson-integral-RC superscript 𝑇 2 𝜃 superscript 𝑀 2 superscript 𝑇 2 subscript ℎ 0 superscript subscript 𝑚 1 superscript 2 𝑚 subscript ℎ 𝑚 subscript ℎ 𝑚 1 {\displaystyle{\displaystyle 2R_{G}\left(t_{0}^{2},t_{0}^{2}+\theta c_{0}^{2},% t_{0}^{2}+\theta a_{0}^{2}\right)=\left(t_{0}^{2}+\theta\sum_{m=0}^{\infty}2^{% m-1}c_{m}^{2}\right)R_{C}\left(T^{2}+\theta M^{2},T^{2}\right)+h_{0}+\sum_{m=1% }^{\infty}2^{m}(h_{m}-h_{m-1}).}}
    0 references
    DLMF id
    DLMF:19.36.E13
    0 references
    Symbols used
    Carlson’s combination of inverse circular and inverse hyperbolic functions
    Defining formula
    R C ⁡ ( x , y ) Carlson-integral-RC 𝑥 𝑦 {\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}
    xml-id
    C19.S2.E17.m2abdec
    0 references
    symmetric elliptic integral of second kind
    Defining formula
    R G ⁡ ( x , y , z ) Carlson-integral-RG 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E3.m2adec
    0 references
    Q11818
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C19.S1.XMD2.m1dec
    0 references
    Q11942
    Defining formula
    M 𝑀 {\displaystyle{\displaystyle M}}
    xml-id
    C19.S36.XMD1.m1cdec
    0 references
    Q11943
    Defining formula
    T 𝑇 {\displaystyle{\displaystyle T}}
    xml-id
    C19.S36.XMD2.m1cdec
    0 references
    Q11944
    Defining formula
    h n subscript ℎ 𝑛 {\displaystyle{\displaystyle h_{n}}}
    xml-id
    C19.S36.XMD3.m1adec
    0 references
     
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