DLMF:25.14.E4 (Q7743): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12149 / rank
 
Normal rank
Property / Symbols used: Q12149 / qualifier
 
Defining formula:

s 𝑠 {\displaystyle{\displaystyle s}}

s
Property / Symbols used: Q12149 / qualifier
 
xml-id: C25.S1.XMD7.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12156 / rank
 
Normal rank
Property / Symbols used: Q12156 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q12156 / qualifier
 
xml-id: C25.S1.XMD8.m1bdec

Latest revision as of 01:02, 2 January 2020

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DLMF:25.14.E4
No description defined

    Statements

    Defining formula
    Φ ⁡ ( z , s , a ) = z m ⁢ Φ ⁡ ( z , s , a + m ) + ∑ n = 0 m - 1 z n ( a + n ) s . Lerch-Phi 𝑧 𝑠 𝑎 superscript 𝑧 𝑚 Lerch-Phi 𝑧 𝑠 𝑎 𝑚 superscript subscript 𝑛 0 𝑚 1 superscript 𝑧 𝑛 superscript 𝑎 𝑛 𝑠 {\displaystyle{\displaystyle\Phi\left(z,s,a\right)=z^{m}\Phi\left(z,s,a+m% \right)+\sum_{n=0}^{m-1}\frac{z^{n}}{(a+n)^{s}}.}}
    0 references
    DLMF id
    DLMF:25.14.E4
    0 references
    Symbols used
    Lerch’s transcendent
    Defining formula
    Φ ⁡ ( z , s , a ) Lerch-Phi 𝑧 𝑠 𝑎 {\displaystyle{\displaystyle\Phi\left(\NVar{z},\NVar{s},\NVar{a}\right)}}
    xml-id
    C25.S14.E1.m2acdec
    0 references
    Q12151
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C25.S1.XMD2.m1dec
    0 references
    Q12148
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C25.S1.XMD3.m1adec
    0 references
    Q12161
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C25.S1.XMD6.m1bdec
    0 references
    Q12149
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C25.S1.XMD7.m1cdec
    0 references
    Q12156
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C25.S1.XMD8.m1bdec
    0 references
     
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