DLMF:15.16.E3 (Q5180): Difference between revisions

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Property / constraint
 

| z + ζ - z ⁢ ζ | < 1 𝑧 𝜁 𝑧 𝜁 1 {\displaystyle{\displaystyle|z+\zeta-z\zeta|<1}}

|z+\zeta-z\zeta|<1
Property / constraint: | z + ζ - z ⁢ ζ | < 1 𝑧 𝜁 𝑧 𝜁 1 {\displaystyle{\displaystyle|z+\zeta-z\zeta|<1}} / rank
 
Normal rank

Revision as of 16:57, 30 December 2019

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DLMF:15.16.E3
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    Statements

    test
    F ⁡ ( a , b c ; z ) ⁢ F ⁡ ( a , b c ; ζ ) = ∑ s = 0 ∞ ( a ) s ⁢ ( b ) s ⁢ ( c - a ) s ⁢ ( c - b ) s ( c ) s ⁢ ( c ) 2 ⁢ s ⁢ s ! ⁢ ( z ⁢ ζ ) s ⁢ F ⁡ ( a + s , b + s c + 2 ⁢ s ; z + ζ - z ⁢ ζ ) , Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝜁 superscript subscript 𝑠 0 Pochhammer 𝑎 𝑠 Pochhammer 𝑏 𝑠 Pochhammer 𝑐 𝑎 𝑠 Pochhammer 𝑐 𝑏 𝑠 Pochhammer 𝑐 𝑠 Pochhammer 𝑐 2 𝑠 𝑠 superscript 𝑧 𝜁 𝑠 Gauss-hypergeometric-F 𝑎 𝑠 𝑏 𝑠 𝑐 2 𝑠 𝑧 𝜁 𝑧 𝜁 {\displaystyle{\displaystyle F\left({a,b\atop c};z\right)F\left({a,b\atop c};% \zeta\right)=\sum_{s=0}^{\infty}\frac{{\left(a\right)_{s}}{\left(b\right)_{s}}% {\left(c-a\right)_{s}}{\left(c-b\right)_{s}}}{{\left(c\right)_{s}}{\left(c% \right)_{2s}}s!}\left(z\zeta\right)^{s}F\left({a+s,b+s\atop c+2s};z+\zeta-z% \zeta\right),}}
    0 references
    DLMF id
    DLMF:15.16.E3
    0 references
    constraint
    | z + ζ - z ⁢ ζ | < 1 𝑧 𝜁 𝑧 𝜁 1 {\displaystyle{\displaystyle|z+\zeta-z\zeta|<1}}
    0 references
     
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