DLMF:13.7.E10 (Q4422): 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.m1aedec
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: 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: Q11558 / rank
 
Normal rank
Property / Symbols used: Q11558 / qualifier
 
test:

s 𝑠 {\displaystyle{\displaystyle s}}

s
Property / Symbols used: Q11558 / qualifier
 
xml-id: C13.S1.XMD3.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11557 / rank
 
Normal rank
Property / Symbols used: Q11557 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11557 / qualifier
 
xml-id: C13.S1.XMD6.m1gdec
Property / Symbols used
 
Property / Symbols used: remainder (locally) / rank
 
Normal rank
Property / Symbols used: remainder (locally) / qualifier
 
test:

R n ⁢ ( a , b , z ) subscript 𝑅 𝑛 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle R_{n}(a,b,z)}}

R_{n}(a,b,z)
Property / Symbols used: remainder (locally) / qualifier
 
xml-id: C13.S7.XMD9.m1dec

Latest revision as of 14:55, 2 January 2020

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English
DLMF:13.7.E10
No description defined

    Statements

    test
    U ⁡ ( a , b , z ) = z - a ⁢ ∑ s = 0 n - 1 ( a ) s ⁢ ( a - b + 1 ) s s ! ⁢ ( - z ) - s + R n ⁢ ( a , b , z ) , Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 𝑧 𝑎 superscript subscript 𝑠 0 𝑛 1 Pochhammer 𝑎 𝑠 Pochhammer 𝑎 𝑏 1 𝑠 𝑠 superscript 𝑧 𝑠 subscript 𝑅 𝑛 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(a,b,z\right)=z^{-a}\sum_{s=0}^{n-1}\frac{{% \left(a\right)_{s}}{\left(a-b+1\right)_{s}}}{s!}(-z)^{-s}+R_{n}(a,b,z),}}
    0 references
    DLMF id
    DLMF:13.7.E10
    0 references
    Symbols used
    Kummer confluent hypergeometric function
    test
    U ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E6.m2acdec
    0 references
    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1aedec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aedec
    0 references
    Q11559
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1ddec
    0 references
    Q11558
    test
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C13.S1.XMD3.m1ddec
    0 references
    Q11557
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1gdec
    0 references
    remainder (locally)
    test
    R n ⁢ ( a , b , z ) subscript 𝑅 𝑛 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle R_{n}(a,b,z)}}
    xml-id
    C13.S7.XMD9.m1dec
    0 references
     
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