DLMF:10.18.E17 (Q3210): Difference between revisions

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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.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
 
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.m2agdec
Property / Symbols used
 
Property / Symbols used: modulus of Bessel functions / rank
 
Normal rank
Property / Symbols used: modulus of Bessel functions / qualifier
 
Defining formula:

M ν ⁡ ( x ) modulus-Bessel-M 𝜈 𝑥 {\displaystyle{\displaystyle M_{\NVar{\nu}}\left(\NVar{x}\right)}}

\HankelmodM{\NVar{\nu}}@{\NVar{x}}
Property / Symbols used: modulus of Bessel functions / qualifier
 
xml-id: C10.S18.E1.m2akdec
Property / Symbols used
 
Property / Symbols used: Q11435 / rank
 
Normal rank
Property / Symbols used: Q11435 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11435 / qualifier
 
xml-id: C10.S1.XMD4.m1pdec
Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1pdec

Latest revision as of 15:35, 2 January 2020

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DLMF:10.18.E17
No description defined

    Statements

    Defining formula
    M ν 2 ⁡ ( x ) ∼ 2 π ⁢ x ⁢ ( 1 + 1 2 ⁢ μ - 1 ( 2 ⁢ x ) 2 + 1 ⋅ 3 2 ⋅ 4 ⁢ ( μ - 1 ) ⁢ ( μ - 9 ) ( 2 ⁢ x ) 4 + 1 ⋅ 3 ⋅ 5 2 ⋅ 4 ⋅ 6 ⁢ ( μ - 1 ) ⁢ ( μ - 9 ) ⁢ ( μ - 25 ) ( 2 ⁢ x ) 6 + ⋯ ) , asymptotic-expansion modulus-Bessel-M 𝜈 2 𝑥 2 𝜋 𝑥 1 1 2 𝜇 1 superscript 2 𝑥 2 ⋅ 1 3 ⋅ 2 4 𝜇 1 𝜇 9 superscript 2 𝑥 4 ⋅ 1 3 5 ⋅ 2 4 6 𝜇 1 𝜇 9 𝜇 25 superscript 2 𝑥 6 ⋯ {\displaystyle{\displaystyle{M_{\nu}^{2}}\left(x\right)\sim\frac{2}{\pi x}% \left(1+\frac{1}{2}\frac{\mu-1}{(2x)^{2}}+\frac{1\cdot 3}{2\cdot 4}\frac{(\mu-% 1)(\mu-9)}{(2x)^{4}}+\frac{1\cdot 3\cdot 5}{2\cdot 4\cdot 6}\frac{(\mu-1)(\mu-% 9)(\mu-25)}{(2x)^{6}}+\cdots\right),}}
    0 references
    DLMF id
    DLMF:10.18.E17
    0 references
    Symbols used
    Q10931
    Defining formula
    ∼ 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
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2agdec
    0 references
    modulus of Bessel functions
    Defining formula
    M ν ⁡ ( x ) modulus-Bessel-M 𝜈 𝑥 {\displaystyle{\displaystyle M_{\NVar{\nu}}\left(\NVar{x}\right)}}
    xml-id
    C10.S18.E1.m2akdec
    0 references
    Q11435
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1pdec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1pdec
    0 references
     
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