DLMF:15.11.E1 (Q5153)

From DRMF
Revision as of 14:21, 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:15.11.E1
No description defined

    Statements

    Defining formula
    d 2 w d z 2 + ( 1 - a 1 - a 2 z - α + 1 - b 1 - b 2 z - β + 1 - c 1 - c 2 z - γ ) ⁢ d w d z + ( ( α - β ) ⁢ ( α - γ ) ⁢ a 1 ⁢ a 2 z - α + ( β - α ) ⁢ ( β - γ ) ⁢ b 1 ⁢ b 2 z - β + ( γ - α ) ⁢ ( γ - β ) ⁢ c 1 ⁢ c 2 z - γ ) ⁢ w ( z - α ) ⁢ ( z - β ) ⁢ ( z - γ ) = 0 , derivative 𝑤 𝑧 2 1 subscript 𝑎 1 subscript 𝑎 2 𝑧 𝛼 1 subscript 𝑏 1 subscript 𝑏 2 𝑧 𝛽 1 subscript 𝑐 1 subscript 𝑐 2 𝑧 𝛾 derivative 𝑤 𝑧 𝛼 𝛽 𝛼 𝛾 subscript 𝑎 1 subscript 𝑎 2 𝑧 𝛼 𝛽 𝛼 𝛽 𝛾 subscript 𝑏 1 subscript 𝑏 2 𝑧 𝛽 𝛾 𝛼 𝛾 𝛽 subscript 𝑐 1 subscript 𝑐 2 𝑧 𝛾 𝑤 𝑧 𝛼 𝑧 𝛽 𝑧 𝛾 0 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}+\left(% \frac{1-a_{1}-a_{2}}{z-\alpha}+\frac{1-b_{1}-b_{2}}{z-\beta}+\frac{1-c_{1}-c_{% 2}}{z-\gamma}\right)\frac{\mathrm{d}w}{\mathrm{d}z}+{\left(\frac{(\alpha-\beta% )(\alpha-\gamma)a_{1}a_{2}}{z-\alpha}+\frac{(\beta-\alpha)(\beta-\gamma)b_{1}b% _{2}}{z-\beta}+\frac{(\gamma-\alpha)(\gamma-\beta)c_{1}c_{2}}{z-\gamma}\right)% \frac{w}{(z-\alpha)(z-\beta)(z-\gamma)}=0},}}
    0 references
    DLMF id
    DLMF:15.11.E1
    0 references
    Symbols used
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2adec
    0 references
    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1dec
    0 references
    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1dec
    0 references
    Q11646
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1dec
    0 references
    Q11647
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1dec
    0 references
    Q11668
    Defining formula
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C15.S11.XMD1.m1dec
    0 references
    Q11669
    Defining formula
    β 𝛽 {\displaystyle{\displaystyle\beta}}
    xml-id
    C15.S11.XMD2.m1dec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5153&oldid=46231"