DLMF:11.11.E8 (Q4069): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
(8 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q10931 / rank
 
Normal rank
Property / Symbols used: Q10931 / qualifier
 
Defining formula:

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

\asympexp
Property / Symbols used: Q10931 / qualifier
 
xml-id: C2.S1.SS3.p1.m11acdec
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
 
Defining formula:

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.m2afdec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5adec
Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
Defining formula:

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

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1adec
Property / Symbols used
 
Property / Symbols used: Q11492 / rank
 
Normal rank
Property / Symbols used: Q11492 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11492 / qualifier
 
xml-id: C11.S1.XMD3.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11497 / rank
 
Normal rank
Property / Symbols used: Q11497 / qualifier
 
Defining formula:

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
 
Defining formula:

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

\delta
Property / Symbols used: Q11498 / qualifier
 
xml-id: C11.S1.XMD6.m1dec
Property / Symbols used
 
Property / Symbols used: Q11510 / rank
 
Normal rank
Property / Symbols used: Q11510 / qualifier
 
Defining formula:

λ 𝜆 {\displaystyle{\displaystyle\lambda}}

\lambda
Property / Symbols used: Q11510 / qualifier
 
xml-id: C11.S11.XMD3.m1dec
Property / Symbols used
 
Property / Symbols used: Q11511 / rank
 
Normal rank
Property / Symbols used: Q11511 / qualifier
 
Defining formula:

a k ⁢ ( λ ) subscript 𝑎 𝑘 𝜆 {\displaystyle{\displaystyle a_{k}(\lambda)}}

a_{k}(\lambda)
Property / Symbols used: Q11511 / qualifier
 
xml-id: C11.S11.XMD4.m1dec

Latest revision as of 15:01, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:11.11.E8
No description defined

    Statements

    Defining formula
    𝐀 ν ⁡ ( λ ⁢ ν ) ∼ 1 π ⁢ ∑ k = 0 ∞ ( 2 ⁢ k ) ! ⁢ a k ⁢ ( λ ) ν 2 ⁢ k + 1 , asymptotic-expansion associated-Anger-Weber-A 𝜈 𝜆 𝜈 1 𝜋 superscript subscript 𝑘 0 2 𝑘 subscript 𝑎 𝑘 𝜆 superscript 𝜈 2 𝑘 1 {\displaystyle{\displaystyle\mathbf{A}_{\nu}\left(\lambda\nu\right)\sim\frac{1% }{\pi}\sum_{k=0}^{\infty}\frac{(2k)!\,a_{k}(\lambda)}{\nu^{2k+1}},}}
    0 references
    DLMF id
    DLMF:11.11.E8
    0 references
    constraint
    | ph ⁡ ν | ≤ π - δ phase 𝜈 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}\nu|\leq\pi-\delta}}
    0 references
    | ph ⁡ ν | ≤ π - δ ph 𝜈 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}\nu|\leq\pi-\delta}}
    0 references
    < π absent 𝜋 {\displaystyle{\displaystyle<\pi}}
    0 references
    Symbols used
    Anger–Weber function
    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.m2aadec
    0 references
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
    0 references
    Q11492
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1fdec
    0 references
    Q11497
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C11.S1.XMD5.m1ddec
    0 references
    Q11498
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C11.S1.XMD6.m1dec
    0 references
    Q11510
    Defining formula
    λ 𝜆 {\displaystyle{\displaystyle\lambda}}
    xml-id
    C11.S11.XMD3.m1dec
    0 references
    Q11511
    Defining formula
    a k ⁢ ( λ ) subscript 𝑎 𝑘 𝜆 {\displaystyle{\displaystyle a_{k}(\lambda)}}
    xml-id
    C11.S11.XMD4.m1dec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4069&oldid=53470"