DLMF:31.10.E11 (Q9062)

From DRMF
Revision as of 13:37, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:31.10.E11
No description defined

    Statements

    Defining formula
    𝒦 ⁢ ( z , t ) = ( z ⁢ t - a ) 1 2 - δ - σ ⁢ ( z ⁢ t / a ) - 1 2 + δ + σ - α ⁢ F 1 2 ⁡ ( 1 2 - δ - σ + α , 3 2 - δ - σ + α - γ α - β + 1 ; a z ⁢ t ) ⁢ P ⁡ { 0 1 ∞ 0 0 - 1 2 + δ + σ ( z - a ) ⁢ ( t - a ) ( 1 - a ) ⁢ ( z ⁢ t - a ) 1 - ϵ 1 - δ - 1 2 + ϵ - σ } . 𝒦 𝑧 𝑡 superscript 𝑧 𝑡 𝑎 1 2 𝛿 𝜎 superscript 𝑧 𝑡 𝑎 1 2 𝛿 𝜎 𝛼 Gauss-hypergeometric-F-as-2F1 1 2 𝛿 𝜎 𝛼 3 2 𝛿 𝜎 𝛼 𝛾 𝛼 𝛽 1 𝑎 𝑧 𝑡 Riemann-P-symbol 0 1 absent 0 0 1 2 𝛿 𝜎 𝑧 𝑎 𝑡 𝑎 1 𝑎 𝑧 𝑡 𝑎 1 italic-ϵ 1 𝛿 1 2 italic-ϵ 𝜎 absent {\displaystyle{\displaystyle\mathcal{K}(z,t)=(zt-a)^{\frac{1}{2}-\delta-\sigma% }\left(\ifrac{zt}{a}\right)^{-\frac{1}{2}+\delta+\sigma-\alpha}\*{{}_{2}F_{1}}% \left({\frac{1}{2}-\delta-\sigma+\alpha,\frac{3}{2}-\delta-\sigma+\alpha-% \gamma\atop\alpha-\beta+1};\frac{a}{zt}\right)\*P\begin{Bmatrix}0&1&\infty&\\ 0&0&-\frac{1}{2}+\delta+\sigma&\dfrac{(z-a)(t-a)}{(1-a)(zt-a)}\\ 1-\epsilon&1-\delta&-\frac{1}{2}+\epsilon-\sigma&\end{Bmatrix}.}}
    0 references
    DLMF id
    DLMF:31.10.E11
    0 references
    Symbols used
    Q11581
    Defining formula
    F 1 2 ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F-as-2F1 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}
    xml-id
    C16.S2.m5aadec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q9062&oldid=38277"