DLMF:10.17.E3 (Q3172): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older editNewer edit →
imported>Admin
imported>Admin
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2aadec

Revision as of 14:28, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:10.17.E3
No description defined

    Statements

    test
    J ν ⁡ ( z ) ∼ ( 2 π ⁢ z ) 1 2 ⁢ ( cos ⁡ ω ⁢ ∑ k = 0 ∞ ( - 1 ) k ⁢ a 2 ⁢ k ⁢ ( ν ) z 2 ⁢ k - sin ⁡ ω ⁢ ∑ k = 0 ∞ ( - 1 ) k ⁢ a 2 ⁢ k + 1 ⁢ ( ν ) z 2 ⁢ k + 1 ) , asymptotic-expansion Bessel-J 𝜈 𝑧 superscript 2 𝜋 𝑧 1 2 𝜔 superscript subscript 𝑘 0 superscript 1 𝑘 subscript 𝑎 2 𝑘 𝜈 superscript 𝑧 2 𝑘 𝜔 superscript subscript 𝑘 0 superscript 1 𝑘 subscript 𝑎 2 𝑘 1 𝜈 superscript 𝑧 2 𝑘 1 {\displaystyle{\displaystyle J_{\nu}\left(z\right)\sim\left(\frac{2}{\pi z}% \right)^{\frac{1}{2}}\*\left(\cos\omega\sum_{k=0}^{\infty}(-1)^{k}\frac{a_{2k}% (\nu)}{z^{2k}}-\sin\omega\sum_{k=0}^{\infty}(-1)^{k}\frac{a_{2k+1}(\nu)}{z^{2k% +1}}\right),}}
    0 references
    DLMF id
    DLMF:10.17.E3
    0 references
    constraint
    | ph ⁡ z | ≤ π - δ phase 𝑧 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi-\delta}}
    0 references
    Symbols used
    Bessel function of the first kind
    test
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2adec
    0 references
    Q10931
    test
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11adec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q3172&oldid=16703"