DLMF:11.11.E4 (Q4761): Difference between revisions

From MaRDI portal
← Older editNewer edit →
‎Changed an Item: Mark DLMF formulae as such
Added link to MaRDI item.
links / mardi / namelinks / mardi / name
 

Revision as of 17:55, 11 July 2023

No description defined
Language Label Description Also known as
English
DLMF:11.11.E4
No description defined

    Statements

    DLMF defining formula
    𝐀 ν ⁡ ( z ) ∼ 1 π ⁢ z ⁢ ∑ k = 0 ∞ F k ⁢ ( ν ) z 2 ⁢ k - ν π ⁢ z 2 ⁢ ∑ k = 0 ∞ G k ⁢ ( ν ) z 2 ⁢ k . asymptotic-expansion associated-Anger-Weber-A 𝜈 𝑧 1 𝜋 𝑧 superscript subscript 𝑘 0 subscript 𝐹 𝑘 𝜈 superscript 𝑧 2 𝑘 𝜈 𝜋 superscript 𝑧 2 superscript subscript 𝑘 0 subscript 𝐺 𝑘 𝜈 superscript 𝑧 2 𝑘 {\displaystyle{\displaystyle\mathbf{A}_{\nu}\left(z\right)\sim\frac{1}{\pi z}% \sum_{k=0}^{\infty}\frac{F_{k}(\nu)}{z^{2k}}-\frac{\nu}{\pi z^{2}}\sum_{k=0}^{% \infty}\frac{G_{k}(\nu)}{z^{2k}}.}}
    0 references
    Symbols used
    Anger–Weber function
    DLMF defining formula
    𝐀 ν ⁡ ( z ) associated-Anger-Weber-A 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{A}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E4.m2adec
    0 references
    Q10905
    DLMF defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1bdec
    0 references
    real or complex order
    DLMF defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1cdec
    0 references
    nonnegative integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C11.S1.XMD5.m1cdec
    0 references
    expansion functions
    DLMF defining formula
    F k ⁢ ( ν ) subscript 𝐹 𝑘 𝜈 {\displaystyle{\displaystyle F_{k}(\nu)}}
    xml-id
    C11.S11.XMD1.m1cdec
    0 references
    expansion functions
    DLMF defining formula
    G k ⁢ ( ν ) subscript 𝐺 𝑘 𝜈 {\displaystyle{\displaystyle G_{k}(\nu)}}
    xml-id
    C11.S11.XMD2.m1cdec
    0 references

    Identifiers

     
    Retrieved from "https://mardi.schubotz.org/w/index.php?title=Item:Q4761&oldid=1343911"
    Powered by MediaWiki