DLMF:12.13.E3 (Q4232): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11517 / rank
 
Normal rank
Property / Symbols used: Q11517 / qualifier
 
Defining formula:

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

\paraV@{\NVar{a}}{\NVar{z}}
Property / Symbols used: Q11517 / qualifier
 
xml-id: C12.S2.SS1.p1.m2adec
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.m1bdec
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.m1bdec
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.m1bdec

Latest revision as of 15:25, 2 January 2020

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DLMF:12.13.E3
No description defined

    Statements

    Defining formula
    V ⁡ ( a , x + y ) = e 1 2 ⁢ x ⁢ y + 1 4 ⁢ y 2 ⁢ ∑ m = 0 ∞ ( a - 1 2 m ) ⁢ y m ⁢ V ⁡ ( a - m , x ) , parabolic-V 𝑎 𝑥 𝑦 superscript 𝑒 1 2 𝑥 𝑦 1 4 superscript 𝑦 2 superscript subscript 𝑚 0 binomial 𝑎 1 2 𝑚 superscript 𝑦 𝑚 parabolic-V 𝑎 𝑚 𝑥 {\displaystyle{\displaystyle V\left(a,x+y\right)=e^{\frac{1}{2}xy+\frac{1}{4}y% ^{2}}\sum_{m=0}^{\infty}\genfrac{(}{)}{0.0pt}{}{a-\tfrac{1}{2}}{m}y^{m}V\left(% a-m,x\right),}}
    0 references
    DLMF id
    DLMF:12.13.E3
    0 references
    Symbols used
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1aadec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    Q11517
    Defining formula
    V ⁡ ( a , z ) parabolic-V 𝑎 𝑧 {\displaystyle{\displaystyle V\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C12.S2.SS1.p1.m2adec
    0 references
    Q11520
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C12.S1.XMD1.m1bdec
    0 references
    Q11542
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C12.S1.XMD2.m1bdec
    0 references
    Q11516
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C12.S1.XMD6.m1bdec
    0 references
     
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