DLMF:11.11.E11 (Q4075): Difference between revisions

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Property / constraint
 

ν → + ∞ → 𝜈 {\displaystyle{\displaystyle\nu\to+\infty}}

\nu\to+\infty
Property / constraint: ν → + ∞ → 𝜈 {\displaystyle{\displaystyle\nu\to+\infty}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Anger–Weber function / rank
 
Normal rank
Property / Symbols used: Anger–Weber function / qualifier
 
test:

𝐀 ν ⁡ ( z ) associated-Anger-Weber-A 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{A}_{\NVar{\nu}}\left(\NVar{z}\right)}}

\AngerWeberA{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Anger–Weber function / qualifier
 
xml-id: C11.S10.E4.m2acdec
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.m11aedec
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.m2ahdec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2adec
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.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11510 / rank
 
Normal rank
Property / Symbols used: Q11510 / qualifier
 
test:

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

\lambda
Property / Symbols used: Q11510 / qualifier
 
xml-id: C11.S11.XMD3.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11512 / rank
 
Normal rank
Property / Symbols used: Q11512 / qualifier
 
test:

b k ⁢ ( λ ) subscript 𝑏 𝑘 𝜆 {\displaystyle{\displaystyle b_{k}(\lambda)}}

b_{k}(\lambda)
Property / Symbols used: Q11512 / qualifier
 
xml-id: C11.S11.XMD5.m1dec

Latest revision as of 14:02, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:11.11.E11
No description defined

    Statements

    test
    𝐀 - ν ⁡ ( λ ⁢ ν ) ∼ ( 2 π ⁢ ν ) 1 / 2 ⁢ e - ν ⁢ μ ⁢ ∑ k = 0 ∞ ( 1 2 ) k ⁢ b k ⁢ ( λ ) ν k , asymptotic-expansion associated-Anger-Weber-A 𝜈 𝜆 𝜈 superscript 2 𝜋 𝜈 1 2 superscript 𝑒 𝜈 𝜇 superscript subscript 𝑘 0 subscript 1 2 𝑘 subscript 𝑏 𝑘 𝜆 superscript 𝜈 𝑘 {\displaystyle{\displaystyle\mathbf{A}_{-\nu}\left(\lambda\nu\right)\sim\left(% \frac{2}{\pi\nu}\right)^{1/2}e^{-\nu\mu}\sum_{k=0}^{\infty}\frac{(\tfrac{1}{2}% )_{k}b_{k}(\lambda)}{\nu^{k}},}}
    0 references
    DLMF id
    DLMF:11.11.E11
    0 references
    constraint
    ν → + ∞ → 𝜈 {\displaystyle{\displaystyle\nu\to+\infty}}
    0 references
    Symbols used
    Anger–Weber function
    test
    𝐀 ν ⁡ ( z ) associated-Anger-Weber-A 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{A}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E4.m2acdec
    0 references
    Q10931
    test
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aedec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ahdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    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.m1fdec
    0 references
    Q11510
    test
    λ 𝜆 {\displaystyle{\displaystyle\lambda}}
    xml-id
    C11.S11.XMD3.m1cdec
    0 references
    Q11512
    test
    b k ⁢ ( λ ) subscript 𝑏 𝑘 𝜆 {\displaystyle{\displaystyle b_{k}(\lambda)}}
    xml-id
    C11.S11.XMD5.m1dec
    0 references
     
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