DLMF:25.11.E45 (Q7719): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10931 / rank
 
Normal rank
Property / Symbols used: Q10931 / qualifier
 
Defining formula:

∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}

\asympexp
Property / Symbols used: Q10931 / qualifier
 
xml-id: C2.S1.SS3.p1.m11abdec

Revision as of 13:47, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:25.11.E45
No description defined

    Statements

    Defining formula
    ζ ′ ⁡ ( - 2 , a ) - 1 12 ⁢ a + 1 9 ⁢ a 3 - ( 1 6 ⁢ a - 1 2 ⁢ a 2 + 1 3 ⁢ a 3 ) ⁢ ln ⁡ a ∼ ∑ k = 1 ∞ 2 ⁢ B 2 ⁢ k + 2 ( 2 ⁢ k + 2 ) ⁢ ( 2 ⁢ k + 1 ) ⁢ 2 ⁢ k ⁢ ( 2 ⁢ k - 1 ) ⁢ a - ( 2 ⁢ k - 1 ) . asymptotic-expansion diffop Hurwitz-zeta 1 2 𝑎 1 12 𝑎 1 9 superscript 𝑎 3 1 6 𝑎 1 2 superscript 𝑎 2 1 3 superscript 𝑎 3 𝑎 superscript subscript 𝑘 1 2 Bernoulli-number-B 2 𝑘 2 2 𝑘 2 2 𝑘 1 2 𝑘 2 𝑘 1 superscript 𝑎 2 𝑘 1 {\displaystyle{\displaystyle\zeta'\left(-2,a\right)-\frac{1}{12}a+\frac{1}{9}a% ^{3}-\left(\frac{1}{6}a-\frac{1}{2}a^{2}+\frac{1}{3}a^{3}\right)\ln a\sim\sum_% {k=1}^{\infty}\frac{2B_{2k+2}}{(2k+2)(2k+1)2k(2k-1)}a^{-(2k-1)}.}}
    0 references
    DLMF id
    DLMF:25.11.E45
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1aldec
    0 references
    Hurwitz zeta function
    Defining formula
    ζ ⁡ ( s , a ) Hurwitz-zeta 𝑠 𝑎 {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}
    xml-id
    C25.S11.E1.m2aardec
    0 references
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11abdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7719&oldid=40040"