DLMF:13.26.E6 (Q4658): 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
 
test:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2aedec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5aedec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
test:

ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1aadec
Property / Symbols used
 
Property / Symbols used: Q11559 / rank
 
Normal rank
Property / Symbols used: Q11559 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11559 / qualifier
 
xml-id: C13.S1.XMD2.m1edec
Property / Symbols used
 
Property / Symbols used: Q11566 / rank
 
Normal rank
Property / Symbols used: Q11566 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11566 / qualifier
 
xml-id: C13.S1.XMD4.m1edec
Property / Symbols used
 
Property / Symbols used: Q11580 / rank
 
Normal rank
Property / Symbols used: Q11580 / qualifier
 
test:

y 𝑦 {\displaystyle{\displaystyle y}}

y
Property / Symbols used: Q11580 / qualifier
 
xml-id: C13.S1.XMD5.m1edec

Latest revision as of 00:06, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:13.26.E6
No description defined

    Statements

    test
    e 1 2 ⁢ y ⁢ ( x x + y ) κ ⁢ ∑ n = 0 ∞ ( 1 2 + μ + κ ) n ⁢ y n n ! ⁢ ( x + y ) n ⁢ M κ + n , μ ⁡ ( x ) , superscript 𝑒 1 2 𝑦 superscript 𝑥 𝑥 𝑦 𝜅 superscript subscript 𝑛 0 Pochhammer 1 2 𝜇 𝜅 𝑛 superscript 𝑦 𝑛 𝑛 superscript 𝑥 𝑦 𝑛 Whittaker-confluent-hypergeometric-M 𝜅 𝑛 𝜇 𝑥 {\displaystyle{\displaystyle e^{\frac{1}{2}y}\left(\frac{x}{x+y}\right)^{% \kappa}\sum_{n=0}^{\infty}\frac{{\left(\frac{1}{2}+\mu+\kappa\right)_{n}}y^{n}% }{n!(x+y)^{n}}M_{\kappa+n,\mu}\left(x\right),}}
    0 references
    DLMF id
    DLMF:13.26.E6
    0 references
    constraint
    ℜ ⁡ ( ( y + x ) / x ) > 1 2 𝑦 𝑥 𝑥 1 2 {\displaystyle{\displaystyle\Re((y+x)/x)>\frac{1}{2}}}
    0 references
    Symbols used
    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1aedec
    0 references
    Whittaker confluent hypergeometric function
    test
    M κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E2.m2aedec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aedec
    0 references
    Q10811
    test
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1aadec
    0 references
    Q11559
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1edec
    0 references
    Q11566
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C13.S1.XMD4.m1edec
    0 references
    Q11580
    test
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C13.S1.XMD5.m1edec
    0 references
     
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