DLMF:1.9.E63 (Q345): Difference between revisions

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Property / constraint
 

| z - z 0 | < R 𝑧 subscript 𝑧 0 𝑅 {\displaystyle{\displaystyle\left|z-z_{0}\right|<R}}

\abs{z-z_{0}}<R
Property / constraint: | z - z 0 | < R 𝑧 subscript 𝑧 0 𝑅 {\displaystyle{\displaystyle\left|z-z_{0}\right|<R}} / rank
 
Normal rank
Property / constraint
 

| z - z 0 | < R 𝑧 subscript 𝑧 0 𝑅 {\displaystyle{\displaystyle\left|z-z_{0}\right|<R}}

\left|z-z_{0}\right|<R
Property / constraint: | z - z 0 | < R 𝑧 subscript 𝑧 0 𝑅 {\displaystyle{\displaystyle\left|z-z_{0}\right|<R}} / rank
 
Normal rank
Property / constraint
 

m = 0 , 1 , 2 , … 𝑚 0 1 2 … {\displaystyle{\displaystyle m=0,1,2,\dots}}

m=0,1,2,\dots
Property / constraint: m = 0 , 1 , 2 , … 𝑚 0 1 2 … {\displaystyle{\displaystyle m=0,1,2,\dots}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q10759 / rank
 
Normal rank
Property / Symbols used: Q10759 / qualifier
 
Defining formula:

( 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.m1adec
Property / Symbols used
 
Property / Symbols used: Q10760 / rank
 
Normal rank
Property / Symbols used: Q10760 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q10760 / qualifier
 
xml-id: C1.S1.XMD1.m1ajdec
Property / Symbols used
 
Property / Symbols used: Q10761 / rank
 
Normal rank
Property / Symbols used: Q10761 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q10761 / qualifier
 
xml-id: C1.S1.XMD6.m1dec
Property / Symbols used
 
Property / Symbols used: Q10757 / rank
 
Normal rank
Property / Symbols used: Q10757 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q10757 / qualifier
 
xml-id: C1.S1.XMD7.m1ndec
Property / Symbols used
 
Property / Symbols used: radius of convergence (locally) / rank
 
Normal rank
Property / Symbols used: radius of convergence (locally) / qualifier
 
Defining formula:

R 𝑅 {\displaystyle{\displaystyle R}}

R
Property / Symbols used: radius of convergence (locally) / qualifier
 
xml-id: C1.S9.XMD23.m1adec

Latest revision as of 16:10, 1 January 2020

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DLMF:1.9.E63
No description defined

    Statements

    Defining formula
    f ( m ) ⁢ ( z ) = ∑ n = 0 ∞ ( n + 1 ) m ⁢ a n + m ⁢ ( z - z 0 ) n , superscript 𝑓 𝑚 𝑧 superscript subscript 𝑛 0 Pochhammer 𝑛 1 𝑚 subscript 𝑎 𝑛 𝑚 superscript 𝑧 subscript 𝑧 0 𝑛 {\displaystyle{\displaystyle f^{(m)}(z)=\sum_{n=0}^{\infty}{\left(n+1\right)_{% m}}a_{n+m}(z-z_{0})^{n},}}
    0 references
    DLMF id
    DLMF:1.9.E63
    0 references
    constraint
    | z - z 0 | < R 𝑧 subscript 𝑧 0 𝑅 {\displaystyle{\displaystyle\left|z-z_{0}\right|<R}}
    0 references
    | z - z 0 | < R 𝑧 subscript 𝑧 0 𝑅 {\displaystyle{\displaystyle\left|z-z_{0}\right|<R}}
    0 references
    m = 0 , 1 , 2 , … 𝑚 0 1 2 … {\displaystyle{\displaystyle m=0,1,2,\dots}}
    0 references
    Symbols used
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
    0 references
    Q10760
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C1.S1.XMD1.m1ajdec
    0 references
    Q10761
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C1.S1.XMD6.m1dec
    0 references
    Q10757
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1ndec
    0 references
    radius of convergence (locally)
    Defining formula
    R 𝑅 {\displaystyle{\displaystyle R}}
    xml-id
    C1.S9.XMD23.m1adec
    0 references
     
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