DLMF:11.9.E9 (Q4017): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older edit
imported>Admin
imported>Admin
 
(10 intermediate revisions by the same user not shown)
Property / constraint
 

z → ∞ → 𝑧 {\displaystyle{\displaystyle z\to\infty}}

z\to\infty
Property / constraint: z → ∞ → 𝑧 {\displaystyle{\displaystyle z\to\infty}} / rank
 
Normal rank
Property / constraint
 

| ph ⁡ z | ≤ π - δ ( < π ) ph 𝑧 annotated 𝜋 𝛿 absent 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi-\delta(<\pi)}}

|\operatorname{ph}z|\leq\pi-\delta(<\pi)
Property / constraint: | ph ⁡ z | ≤ π - δ ( < π ) ph 𝑧 annotated 𝜋 𝛿 absent 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi-\delta(<\pi)}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Lommel function / rank
 
Normal rank
Property / Symbols used: Lommel function / qualifier
 
test:

S μ , ν ⁡ ( z ) Lommel-S 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle S_{{\NVar{\mu}},{\NVar{\nu}}}\left(\NVar{z}\right% )}}

\LommelS{\NVar{\mu}}{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Lommel function / qualifier
 
xml-id: C11.S9.E5.m2abdec
Property / Symbols used
 
Property / Symbols used: Q10931 / rank
 
Normal rank
Property / Symbols used: Q10931 / qualifier
 
test:

∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}

\asympexp
Property / Symbols used: Q10931 / qualifier
 
xml-id: C2.S1.SS3.p1.m11adec
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
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.m1adec
Property / Symbols used
 
Property / Symbols used: Q11491 / rank
 
Normal rank
Property / Symbols used: Q11491 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11491 / qualifier
 
xml-id: C11.S1.XMD2.m1gdec
Property / Symbols used
 
Property / Symbols used: Q11492 / rank
 
Normal rank
Property / Symbols used: Q11492 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11492 / qualifier
 
xml-id: C11.S1.XMD3.m1hdec
Property / Symbols used
 
Property / Symbols used: Q11497 / rank
 
Normal rank
Property / Symbols used: Q11497 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11497 / qualifier
 
xml-id: C11.S1.XMD5.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11498 / rank
 
Normal rank
Property / Symbols used: Q11498 / qualifier
 
test:

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

\delta
Property / Symbols used: Q11498 / qualifier
 
xml-id: C11.S1.XMD6.m1dec
Property / Symbols used
 
Property / Symbols used: Q11505 / rank
 
Normal rank
Property / Symbols used: Q11505 / qualifier
 
test:

a k ⁢ ( μ , ν ) subscript 𝑎 𝑘 𝜇 𝜈 {\displaystyle{\displaystyle a_{k}(\mu,\nu)}}

a_{k}(\mu,\nu)
Property / Symbols used: Q11505 / qualifier
 
xml-id: C11.S9.XMD4.m1dec

Latest revision as of 13:53, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:11.9.E9
No description defined

    Statements

    test
    S μ , ν ⁡ ( z ) ∼ z μ - 1 ⁢ ∑ k = 0 ∞ ( - 1 ) k ⁢ a k ⁢ ( - μ , ν ) ⁢ z - 2 ⁢ k , asymptotic-expansion Lommel-S 𝜇 𝜈 𝑧 superscript 𝑧 𝜇 1 superscript subscript 𝑘 0 superscript 1 𝑘 subscript 𝑎 𝑘 𝜇 𝜈 superscript 𝑧 2 𝑘 {\displaystyle{\displaystyle S_{{\mu},{\nu}}\left(z\right)\sim z^{\mu-1}\sum_{% k=0}^{\infty}(-1)^{k}a_{k}(-\mu,\nu)z^{-2k},}}
    0 references
    DLMF id
    DLMF:11.9.E9
    0 references
    constraint
    | ph ⁡ z | ≤ π - δ ( < π ) phase 𝑧 annotated 𝜋 𝛿 absent 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi-\delta(<\pi)}}
    0 references
    z → ∞ → 𝑧 {\displaystyle{\displaystyle z\to\infty}}
    0 references
    | ph ⁡ z | ≤ π - δ ( < π ) ph 𝑧 annotated 𝜋 𝛿 absent 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi-\delta(<\pi)}}
    0 references
    Symbols used
    Lommel function
    test
    S μ , ν ⁡ ( z ) Lommel-S 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle S_{{\NVar{\mu}},{\NVar{\nu}}}\left(\NVar{z}\right% )}}
    xml-id
    C11.S9.E5.m2abdec
    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
    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
    0 references
    Q11491
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1gdec
    0 references
    Q11492
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1hdec
    0 references
    Q11497
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C11.S1.XMD5.m1ddec
    0 references
    Q11498
    test
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C11.S1.XMD6.m1dec
    0 references
    Q11505
    test
    a k ⁢ ( μ , ν ) subscript 𝑎 𝑘 𝜇 𝜈 {\displaystyle{\displaystyle a_{k}(\mu,\nu)}}
    xml-id
    C11.S9.XMD4.m1dec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q4017&oldid=21548"