DLMF:2.10.E23 (Q1010): Difference between revisions

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Property / constraint
 

x → + ∞ → 𝑥 {\displaystyle{\displaystyle x\to+\infty}}

x\to+\infty
Property / constraint: x → + ∞ → 𝑥 {\displaystyle{\displaystyle x\to+\infty}} / rank
 
Normal rank

Revision as of 16:55, 30 December 2019

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DLMF:2.10.E23
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    Statements

    test
    F 2 0 ⁡ ( - ; 1 , 1 ; x ) = ∫ - 1 / 2 ∞ x t ( Γ ⁡ ( t + 1 ) ) 3 ⁢ d t + 2 ⁢ ℜ ⁡ ∫ - 1 / 2 i ⁢ ∞ x t ( Γ ⁡ ( t + 1 ) ) 3 ⁢ d t e - 2 ⁢ π ⁢ i ⁢ t - 1 = ∫ 0 ∞ x t ( Γ ⁡ ( t + 1 ) ) 3 ⁢ d t + O ⁡ ( 1 ) , Gauss-hypergeometric-pFq 0 2 1 1 𝑥 superscript subscript 1 2 superscript 𝑥 𝑡 superscript Euler-Gamma 𝑡 1 3 𝑡 2 superscript subscript 1 2 𝑖 superscript 𝑥 𝑡 superscript Euler-Gamma 𝑡 1 3 𝑡 superscript 𝑒 2 𝜋 𝑖 𝑡 1 superscript subscript 0 superscript 𝑥 𝑡 superscript Euler-Gamma 𝑡 1 3 𝑡 Big-O 1 {\displaystyle{\displaystyle{{}_{0}F_{2}}\left(-;1,1;x\right)=\int_{-1/2}^{% \infty}\frac{x^{t}}{(\Gamma\left(t+1\right))^{3}}\mathrm{d}t+2\Re\int_{-1/2}^{% i\infty}\frac{x^{t}}{(\Gamma\left(t+1\right))^{3}}\frac{\mathrm{d}t}{e^{-2\pi it% }-1}=\int_{0}^{\infty}\frac{x^{t}}{(\Gamma\left(t+1\right))^{3}}\mathrm{d}t+O% \left(1\right),}}
    0 references
    DLMF id
    DLMF:2.10.E23
    0 references
    constraint
    x → + ∞ → 𝑥 {\displaystyle{\displaystyle x\to+\infty}}
    0 references
     
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