DLMF:11.6.E1 (Q3977): 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: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
Defining formula:

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.m2adec

Revision as of 14:45, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:11.6.E1
No description defined

    Statements

    Defining formula
    𝐊 ν ⁡ ( z ) ∼ 1 π ⁢ ∑ k = 0 ∞ Γ ⁡ ( k + 1 2 ) ⁢ ( 1 2 ⁢ z ) ν - 2 ⁢ k - 1 Γ ⁡ ( ν + 1 2 - k ) , asymptotic-expansion associated-Struve-K 𝜈 𝑧 1 𝜋 superscript subscript 𝑘 0 Euler-Gamma 𝑘 1 2 superscript 1 2 𝑧 𝜈 2 𝑘 1 Euler-Gamma 𝜈 1 2 𝑘 {\displaystyle{\displaystyle\mathbf{K}_{\nu}\left(z\right)\sim\frac{1}{\pi}% \sum_{k=0}^{\infty}\frac{\Gamma\left(k+\tfrac{1}{2}\right)(\tfrac{1}{2}z)^{\nu% -2k-1}}{\Gamma\left(\nu+\tfrac{1}{2}-k\right)},}}
    0 references
    DLMF id
    DLMF:11.6.E1
    0 references
    constraint
    | ph ⁡ z | ≤ π - δ phase 𝑧 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi-\delta}}
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q3977&oldid=50599"