DLMF:12.13.E1 (Q4230): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q11320 / rank
 
Normal rank
Property / Symbols used: Q11320 / qualifier
 
Defining formula:

U ( a , z ) parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}

\paraU@{\NVar{a}}{\NVar{z}}
Property / Symbols used: Q11320 / qualifier
 
xml-id: C12.S2.SS1.p1.m1adec
Property / Symbols used
 
Property / Symbols used: Q11520 / rank
 
Normal rank
Property / Symbols used: Q11520 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11520 / qualifier
 
xml-id: C12.S1.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: Q11542 / rank
 
Normal rank
Property / Symbols used: Q11542 / qualifier
 
Defining formula:

y 𝑦 {\displaystyle{\displaystyle y}}

y
Property / Symbols used: Q11542 / qualifier
 
xml-id: C12.S1.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q11516 / rank
 
Normal rank
Property / Symbols used: Q11516 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11516 / qualifier
 
xml-id: C12.S1.XMD6.m1dec

Latest revision as of 15:25, 2 January 2020

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English
DLMF:12.13.E1
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    Statements

    U ( a , x + y ) = e 1 2 x y + 1 4 y 2 m = 0 ( - y ) m m ! U ( a - m , x ) , parabolic-U 𝑎 𝑥 𝑦 superscript 𝑒 1 2 𝑥 𝑦 1 4 superscript 𝑦 2 superscript subscript 𝑚 0 superscript 𝑦 𝑚 𝑚 parabolic-U 𝑎 𝑚 𝑥 {\displaystyle{\displaystyle U\left(a,x+y\right)=e^{\frac{1}{2}xy+\frac{1}{4}y% ^{2}}\sum_{m=0}^{\infty}\frac{(-y)^{m}}{m!}U\left(a-m,x\right),}}
    0 references
    DLMF:12.13.E1
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2adec
    0 references
    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    U ( a , z ) parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
    C12.S2.SS1.p1.m1adec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C12.S1.XMD1.m1dec
    0 references
    y 𝑦 {\displaystyle{\displaystyle y}}
    C12.S1.XMD2.m1dec
    0 references
    a 𝑎 {\displaystyle{\displaystyle a}}
    C12.S1.XMD6.m1dec
    0 references