DLMF:13.2.E10 (Q4300): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10754 / rank
 
Normal rank
Property / Symbols used: Q10754 / qualifier
 
test:

( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}

\binom{\NVar{m}}{\NVar{n}}
Property / Symbols used: Q10754 / qualifier
 
xml-id: C1.S2.SS1.m1abdec
Property / Symbols used
 
Property / Symbols used: Q11561 / rank
 
Normal rank
Property / Symbols used: Q11561 / qualifier
 
test:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11561 / qualifier
 
xml-id: C13.S1.XMD1.m1adec
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.m1idec

Latest revision as of 14:36, 2 January 2020

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DLMF:13.2.E10
No description defined

    Statements

    test
    U ⁡ ( - m , n + 1 , z ) = ( - 1 ) m ⁢ ( n + 1 ) m ⁢ M ⁡ ( - m , n + 1 , z ) = ( - 1 ) m ⁢ ∑ s = 0 m ( m s ) ⁢ ( n + s + 1 ) m - s ⁢ ( - z ) s . Kummer-confluent-hypergeometric-U 𝑚 𝑛 1 𝑧 superscript 1 𝑚 Pochhammer 𝑛 1 𝑚 Kummer-confluent-hypergeometric-M 𝑚 𝑛 1 𝑧 superscript 1 𝑚 superscript subscript 𝑠 0 𝑚 binomial 𝑚 𝑠 Pochhammer 𝑛 𝑠 1 𝑚 𝑠 superscript 𝑧 𝑠 {\displaystyle{\displaystyle U\left(-m,n+1,z\right)=(-1)^{m}{\left(n+1\right)_% {m}}M\left(-m,n+1,z\right)=(-1)^{m}\sum_{s=0}^{m}\genfrac{(}{)}{0.0pt}{}{m}{s}% {\left(n+s+1\right)_{m-s}}(-z)^{s}.}}
    0 references
    DLMF id
    DLMF:13.2.E10
    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.m2aedec
    0 references
    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.m2addec
    0 references
    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1afdec
    0 references
    Q10754
    test
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1abdec
    0 references
    Q11561
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C13.S1.XMD1.m1adec
    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.m1idec
    0 references
     
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