DLMF:13.2.E15 (Q4305): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11557 / rank
 
Normal rank
Property / Symbols used: Q11557 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11557 / qualifier
 
xml-id: C13.S1.XMD6.m1ndec

Latest revision as of 15:37, 2 January 2020

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DLMF:13.2.E15
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    Statements

    Defining formula
    U ⁡ ( - n + b - 1 , b , z ) = ( - 1 ) n ⁢ ( 2 - b ) n ⁢ z 1 - b + O ⁡ ( z 2 - b ) . Kummer-confluent-hypergeometric-U 𝑛 𝑏 1 𝑏 𝑧 superscript 1 𝑛 Pochhammer 2 𝑏 𝑛 superscript 𝑧 1 𝑏 Big-O superscript 𝑧 2 𝑏 {\displaystyle{\displaystyle U\left(-n+b-1,b,z\right)=(-1)^{n}{\left(2-b\right% )_{n}}z^{1-b}+O\left(z^{2-b}\right).}}
    0 references
    DLMF id
    DLMF:13.2.E15
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2abdec
    0 references
    Kummer confluent hypergeometric function
    Defining formula
    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.m2ahdec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1ahdec
    0 references
    Q11559
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1gdec
    0 references
    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1ndec
    0 references
     
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