DLMF:10.41.E13 (Q3610): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older edit
imported>Admin
imported>Admin
 
(7 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
test:

ph phase {\displaystyle{\displaystyle\operatorname{ph}}}

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1aadec
Property / Symbols used
 
Property / Symbols used: Q11428 / rank
 
Normal rank
Property / Symbols used: Q11428 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11428 / qualifier
 
xml-id: C10.S1.XMD3.m1gdec
Property / Symbols used
 
Property / Symbols used: Q11426 / rank
 
Normal rank
Property / Symbols used: Q11426 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11426 / qualifier
 
xml-id: C10.S1.XMD6.m1jdec
Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1gdec
Property / Symbols used
 
Property / Symbols used: Q11442 / rank
 
Normal rank
Property / Symbols used: Q11442 / qualifier
 
test:

δ 𝛿 {\displaystyle{\displaystyle\delta}}

\delta
Property / Symbols used: Q11442 / qualifier
 
xml-id: C10.S1.XMD8.m1adec
Property / Symbols used
 
Property / Symbols used: DLMF:10.41.E7 / rank
 
Normal rank
Property / Symbols used: DLMF:10.41.E7 / qualifier
 
test:

η 𝜂 {\displaystyle{\displaystyle\eta}}

\eta
Property / Symbols used: DLMF:10.41.E7 / qualifier
 
xml-id: C10.S41.XMD1.m1gdec
Property / Symbols used
 
Property / Symbols used: Q11480 / rank
 
Normal rank
Property / Symbols used: Q11480 / qualifier
 
test:

p 𝑝 {\displaystyle{\displaystyle p}}

p
Property / Symbols used: Q11480 / qualifier
 
xml-id: C10.S41.XMD2.m1adec
Property / Symbols used
 
Property / Symbols used: Q11453 / rank
 
Normal rank
Property / Symbols used: Q11453 / qualifier
 
test:

U k ⁢ ( p ) subscript 𝑈 𝑘 𝑝 {\displaystyle{\displaystyle U_{k}(p)}}

U_{k}(p)
Property / Symbols used: Q11453 / qualifier
 
xml-id: C10.S41.XMD3.m1edec

Latest revision as of 12:58, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:10.41.E13
No description defined

    Statements

    test
    K ν ⁡ ( ν ⁢ z ) = ( π 2 ⁢ ν ) 1 2 ⁢ e - ν ⁢ η ( 1 + z 2 ) 1 4 ⁢ ( ∑ k = 0 ℓ - 1 ( - 1 ) k ⁢ U k ⁢ ( p ) ν k + O ⁡ ( 1 z ℓ ) ) , modified-Bessel-second-kind 𝜈 𝜈 𝑧 superscript 𝜋 2 𝜈 1 2 superscript 𝑒 𝜈 𝜂 superscript 1 superscript 𝑧 2 1 4 superscript subscript 𝑘 0 ℓ 1 superscript 1 𝑘 subscript 𝑈 𝑘 𝑝 superscript 𝜈 𝑘 Big-O 1 superscript 𝑧 ℓ {\displaystyle{\displaystyle K_{\nu}\left(\nu z\right)=\left(\frac{\pi}{2\nu}% \right)^{\frac{1}{2}}\frac{e^{-\nu\eta}}{(1+z^{2})^{\frac{1}{4}}}\*\left(\sum_% {k=0}^{\ell-1}(-1)^{k}\frac{U_{k}(p)}{\nu^{k}}+O\left(\frac{1}{z^{\ell}}\right% )\right),}}
    0 references
    DLMF id
    DLMF:10.41.E13
    0 references
    constraint
    | ph ⁡ z | ≤ 3 2 ⁢ π - δ phase 𝑧 3 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{3}{2}\pi-\delta}}
    0 references
    Symbols used
    order not exceeding
    test
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2agdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2agdec
    0 references
    modified Bessel function of the second kind
    test
    K ν ⁡ ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E3.m2acdec
    0 references
    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1aadec
    0 references
    Q11428
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1gdec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1jdec
    0 references
    Q11427
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1gdec
    0 references
    Q11442
    test
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C10.S1.XMD8.m1adec
    0 references
    DLMF:10.41.E7
    test
    η 𝜂 {\displaystyle{\displaystyle\eta}}
    xml-id
    C10.S41.XMD1.m1gdec
    0 references
    Q11480
    test
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C10.S41.XMD2.m1adec
    0 references
    Q11453
    test
    U k ⁢ ( p ) subscript 𝑈 𝑘 𝑝 {\displaystyle{\displaystyle U_{k}(p)}}
    xml-id
    C10.S41.XMD3.m1edec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q3610&oldid=19358"