DLMF:13.13.E5 (Q4482): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10759 / rank
 
Normal rank
Property / Symbols used: Q10759 / qualifier
 
test:

( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

\Pochhammersym{\NVar{a}}{\NVar{n}}
Property / Symbols used: Q10759 / qualifier
 
xml-id: C5.S2.SS3.m1addec
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.m2aadec
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.m5addec
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.m1ddec
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.m1ddec
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.m1ddec
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

Latest revision as of 15:03, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:13.13.E5
No description defined

    Statements

    test
    e y ⁢ ( x x + y ) b - a ⁢ ∑ n = 0 ∞ ( b - a ) n ⁢ y n n ! ⁢ ( x + y ) n ⁢ M ⁡ ( a - n , b , x ) , superscript 𝑒 𝑦 superscript 𝑥 𝑥 𝑦 𝑏 𝑎 superscript subscript 𝑛 0 Pochhammer 𝑏 𝑎 𝑛 superscript 𝑦 𝑛 𝑛 superscript 𝑥 𝑦 𝑛 Kummer-confluent-hypergeometric-M 𝑎 𝑛 𝑏 𝑥 {\displaystyle{\displaystyle e^{y}\left(\frac{x}{x+y}\right)^{b-a}\sum_{n=0}^{% \infty}\frac{{\left(b-a\right)_{n}}y^{n}}{n!(x+y)^{n}}\*M\left(a-n,b,x\right),}}
    0 references
    DLMF id
    DLMF:13.13.E5
    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
    $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function
    test
    M ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E2.m2addec
    0 references
    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1addec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5addec
    0 references
    Q11559
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1ddec
    0 references
    Q11566
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C13.S1.XMD4.m1ddec
    0 references
    Q11580
    test
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C13.S1.XMD5.m1ddec
    0 references
    Q10811
    test
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1aadec
    0 references
     
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