DLMF:24.4.E31 (Q7444): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12110 / rank
 
Normal rank
Property / Symbols used: Q12110 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12110 / qualifier
 
xml-id: C24.S1.XMD5.m1addec

Latest revision as of 01:28, 2 January 2020

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DLMF:24.4.E31
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    Statements

    Defining formula
    B n ⁡ ( 1 4 ) = ( - 1 ) n ⁢ B n ⁡ ( 3 4 ) = - 1 - 2 1 - n 2 n ⁢ B n - n 4 n ⁢ E n - 1 , Bernoulli-polynomial-B 𝑛 1 4 superscript 1 𝑛 Bernoulli-polynomial-B 𝑛 3 4 1 superscript 2 1 𝑛 superscript 2 𝑛 Bernoulli-number-B 𝑛 𝑛 superscript 4 𝑛 Euler-number-E 𝑛 1 {\displaystyle{\displaystyle B_{n}\left(\tfrac{1}{4}\right)=(-1)^{n}B_{n}\left% (\tfrac{3}{4}\right)=-\frac{1-2^{1-n}}{2^{n}}B_{n}-\frac{n}{4^{n}}E_{n-1},}}
    0 references
    DLMF id
    DLMF:24.4.E31
    0 references
    constraint
    n = 1 , 2 , … 𝑛 1 2 … {\displaystyle{\displaystyle n=1,2,\dots}}
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1akdec
    0 references
    Q11288
    Defining formula
    B n ⁡ ( x ) Bernoulli-polynomial-B 𝑛 𝑥 {\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S2.SS1.m2aodec
    0 references
    Q11238
    Defining formula
    E n Euler-number-E 𝑛 {\displaystyle{\displaystyle E_{\NVar{n}}}}
    xml-id
    C24.S2.SS2.m1addec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1addec
    0 references
     
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