DLMF:10.68.E16 (Q3886): Difference between revisions

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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.m2ahdec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2abdec
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.m1mdec
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.m1ldec

Latest revision as of 14:30, 2 January 2020

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DLMF:10.68.E16
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    Statements

    Defining formula
    M ν ⁡ ( x ) = e x / 2 ( 2 ⁢ π ⁢ x ) 1 2 ⁢ ( 1 - μ - 1 8 ⁢ 2 ⁢ 1 x + ( μ - 1 ) 2 256 ⁢ 1 x 2 - ( μ - 1 ) ⁢ ( μ 2 + 14 ⁢ μ - 399 ) 6144 ⁢ 2 ⁢ 1 x 3 + O ⁡ ( 1 x 4 ) ) , modulus-Bessel-M 𝜈 𝑥 superscript 𝑒 𝑥 2 superscript 2 𝜋 𝑥 1 2 1 𝜇 1 8 2 1 𝑥 superscript 𝜇 1 2 256 1 superscript 𝑥 2 𝜇 1 superscript 𝜇 2 14 𝜇 399 6144 2 1 superscript 𝑥 3 Big-O 1 superscript 𝑥 4 {\displaystyle{\displaystyle M_{\nu}\left(x\right)=\frac{e^{x/\sqrt{2}}}{(2\pi x% )^{\frac{1}{2}}}\left(1-\frac{\mu-1}{8\sqrt{2}}\frac{1}{x}+\frac{(\mu-1)^{2}}{% 256}\frac{1}{x^{2}}-\frac{(\mu-1)(\mu^{2}+14\mu-399)}{6144\sqrt{2}}\frac{1}{x^% {3}}+O\left(\frac{1}{x^{4}}\right)\right),}}
    0 references
    DLMF id
    DLMF:10.68.E16
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ahdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    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.m1mdec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1ldec
    0 references
     
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