DLMF:2.6.E53 (Q879): Difference between revisions

From testwiki
Jump to navigation Jump to search
imported>Admin
 
imported>Admin
 
(4 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2aldec
Property / Symbols used
 
Property / Symbols used: Q10754 / rank
 
Normal rank
Property / Symbols used: Q10754 / qualifier
 
test:

( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}

\binom{\NVar{m}}{\NVar{n}}
Property / Symbols used: Q10754 / qualifier
 
xml-id: C1.S2.SS1.m1addec
Property / Symbols used
 
Property / Symbols used: Q11028 / rank
 
Normal rank
Property / Symbols used: Q11028 / qualifier
 
test:

μ 𝜇 {\displaystyle{\displaystyle\mu}}

\mu
Property / Symbols used: Q11028 / qualifier
 
xml-id: C2.S6.XMD14.m1mdec
Property / Symbols used
 
Property / Symbols used: Q11031 / rank
 
Normal rank
Property / Symbols used: Q11031 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11031 / qualifier
 
xml-id: C2.S6.XMD20.m1kdec
Property / Symbols used
 
Property / Symbols used: Q11036 / rank
 
Normal rank
Property / Symbols used: Q11036 / qualifier
 
test:

δ n ⁢ ( x ) subscript 𝛿 𝑛 𝑥 {\displaystyle{\displaystyle\delta_{n}(x)}}

\delta_{n}(x)
Property / Symbols used: Q11036 / qualifier
 
xml-id: C2.S6.XMD25.m1ddec

Latest revision as of 16:18, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:2.6.E53
No description defined

    Statements

    test
    | δ n ⁢ ( x ) | ≤ Γ ⁡ ( μ + 1 ) ⁢ Γ ⁡ ( 1 - α ) Γ ⁡ ( μ + 1 - α ) ⁢ Γ ⁡ ( n + α ) ⁢ ∑ j = 0 n ( n j ) ⁢ Γ ⁡ ( n + α - j ) | Γ ⁡ ( μ + 1 - j ) | ⁢ x μ - α subscript 𝛿 𝑛 𝑥 Euler-Gamma 𝜇 1 Euler-Gamma 1 𝛼 Euler-Gamma 𝜇 1 𝛼 Euler-Gamma 𝑛 𝛼 superscript subscript 𝑗 0 𝑛 binomial 𝑛 𝑗 Euler-Gamma 𝑛 𝛼 𝑗 Euler-Gamma 𝜇 1 𝑗 superscript 𝑥 𝜇 𝛼 {\displaystyle{\displaystyle{\left|\delta_{n}(x)\right|}\leq\frac{\Gamma\left(% \mu+1\right)\Gamma\left(1-\alpha\right)}{\Gamma\left(\mu+1-\alpha\right)\Gamma% \left(n+\alpha\right)}\*\sum_{j=0}^{n}\dbinom{n}{j}\frac{\Gamma\left(n+\alpha-% j\right)}{\left|\Gamma\left(\mu+1-j\right)\right|}x^{\mu-\alpha}}}
    0 references
    DLMF id
    DLMF:2.6.E53
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aldec
    0 references
    Q10754
    test
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1addec
    0 references
    Q11028
    test
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C2.S6.XMD14.m1mdec
    0 references
    Q11031
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C2.S6.XMD20.m1kdec
    0 references
    Q11036
    test
    δ n ⁢ ( x ) subscript 𝛿 𝑛 𝑥 {\displaystyle{\displaystyle\delta_{n}(x)}}
    xml-id
    C2.S6.XMD25.m1ddec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q879&oldid=4938"