DLMF:13.26.E4 (Q4656): Difference between revisions

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Property / constraint
 

| y | < | x | 𝑦 𝑥 {\displaystyle{\displaystyle|y|<|x|}}

|y|<|x|
Property / constraint: | y | < | x | 𝑦 𝑥 {\displaystyle{\displaystyle|y|<|x|}} / rank
 
Normal rank
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.m1acdec
Property / Symbols used
 
Property / Symbols used: Whittaker confluent hypergeometric function / rank
 
Normal rank
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
 
test:

M κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}

\WhittakerconfhyperM{\NVar{\kappa}}{\NVar{\mu}}@{\NVar{z}}
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
 
xml-id: C13.S14.E2.m2acdec
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.m2acdec
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.m5acdec
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.m1cdec
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.m1cdec
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.m1cdec

Latest revision as of 00:06, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:13.26.E4
No description defined

    Statements

    test
    e 1 2 ⁢ y ⁢ ( x x + y ) μ - 1 2 ⁢ ∑ n = 0 ∞ ( - 2 ⁢ μ ) n n ! ⁢ ( - y x ) n ⁢ M κ + 1 2 ⁢ n , μ - 1 2 ⁢ n ⁡ ( x ) , superscript 𝑒 1 2 𝑦 superscript 𝑥 𝑥 𝑦 𝜇 1 2 superscript subscript 𝑛 0 Pochhammer 2 𝜇 𝑛 𝑛 superscript 𝑦 𝑥 𝑛 Whittaker-confluent-hypergeometric-M 𝜅 1 2 𝑛 𝜇 1 2 𝑛 𝑥 {\displaystyle{\displaystyle e^{\frac{1}{2}y}\left(\frac{x}{x+y}\right)^{\mu-% \frac{1}{2}}\sum_{n=0}^{\infty}\frac{{\left(-2\mu\right)_{n}}}{n!}\left(\frac{% -y}{\sqrt{x}}\right)^{n}\*M_{\kappa+\frac{1}{2}n,\mu-\frac{1}{2}n}\left(x% \right),}}
    0 references
    DLMF id
    DLMF:13.26.E4
    0 references
    constraint
    | y | < | x | 𝑦 𝑥 {\displaystyle{\displaystyle|y|<|x|}}
    0 references
    Symbols used
    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1acdec
    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.m2acdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5acdec
    0 references
    Q11559
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1cdec
    0 references
    Q11566
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C13.S1.XMD4.m1cdec
    0 references
    Q11580
    test
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C13.S1.XMD5.m1cdec
    0 references
     
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