DLMF:25.14.E1 (Q7740): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / constraint
 

| z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}

|z|<1
Property / constraint: | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}} / rank
 
Normal rank
Property / constraint
 

s > 1 , | z | = 1 formulae-sequence 𝑠 1 𝑧 1 {\displaystyle{\displaystyle\Re s>1,|z|=1}}

\Re s>1,|z|=1
Property / constraint: s > 1 , | z | = 1 formulae-sequence 𝑠 1 𝑧 1 {\displaystyle{\displaystyle\Re s>1,|z|=1}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q10769 / rank
 
Normal rank
Property / Symbols used: Q10769 / qualifier
 
Defining formula:

equal-by definition {\displaystyle{\displaystyle\equiv}}

\defeq
Property / Symbols used: Q10769 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r9.m2adec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1adec
Property / Symbols used
 
Property / Symbols used: Q12148 / rank
 
Normal rank
Property / Symbols used: Q12148 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12148 / qualifier
 
xml-id: C25.S1.XMD3.m1dec
Property / Symbols used
 
Property / Symbols used: Q12161 / rank
 
Normal rank
Property / Symbols used: Q12161 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q12161 / qualifier
 
xml-id: C25.S1.XMD6.m1dec
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.m1dec
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.m1dec

Latest revision as of 01:02, 2 January 2020

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DLMF:25.14.E1
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    Statements

    Φ ( z , s , a ) n = 0 z n ( a + n ) s , equal-by definition Lerch-Phi 𝑧 𝑠 𝑎 superscript subscript 𝑛 0 superscript 𝑧 𝑛 superscript 𝑎 𝑛 𝑠 {\displaystyle{\displaystyle{\Phi\left(z,s,a\right)\equiv\sum_{n=0}^{\infty}% \frac{z^{n}}{(a+n)^{s}}},}}
    0 references
    DLMF:25.14.E1
    0 references
    s > 1 , | z | = 1 formulae-sequence 𝑠 1 𝑧 1 {\displaystyle{\displaystyle\Re s>1,|z|=1}}
    0 references
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
    0 references
    s > 1 , | z | = 1 formulae-sequence 𝑠 1 𝑧 1 {\displaystyle{\displaystyle\Re s>1,|z|=1}}
    0 references
    equal-by definition {\displaystyle{\displaystyle\equiv}}
    introduction.Sx4.p1.t1.r9.m2adec
    0 references
    absent {\displaystyle{\displaystyle\Re}}
    C1.S9.E2.m1adec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C25.S1.XMD3.m1dec
    0 references
    a 𝑎 {\displaystyle{\displaystyle a}}
    C25.S1.XMD6.m1dec
    0 references
    s 𝑠 {\displaystyle{\displaystyle s}}
    C25.S1.XMD7.m1dec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C25.S1.XMD8.m1dec
    0 references