DLMF:10.68.E21 (Q3891): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
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.m2amdec
Property / Symbols used
 
Property / Symbols used: Q11445 / rank
 
Normal rank
Property / Symbols used: Q11445 / qualifier
 
Defining formula:

ϕ ν ( x ) phase-Bessel-Phi 𝜈 𝑥 {\displaystyle{\displaystyle\phi_{\NVar{\nu}}\left(\NVar{x}\right)}}

\Hankelphasederivphi{\NVar{\nu}}@{\NVar{x}}
Property / Symbols used: Q11445 / qualifier
 
xml-id: C10.S18.E3.m2addec
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.m1rdec
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.m1qdec

Latest revision as of 14:31, 2 January 2020

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DLMF:10.68.E21
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    Statements

    ϕ ν ( x ) = - x 2 - ( 1 2 ν + 1 8 ) π - μ - 1 8 2 1 x + μ - 1 16 1 x 2 + ( μ - 1 ) ( μ - 25 ) 384 2 1 x 3 + O ( 1 x 5 ) . phase-Bessel-Phi 𝜈 𝑥 𝑥 2 1 2 𝜈 1 8 𝜋 𝜇 1 8 2 1 𝑥 𝜇 1 16 1 superscript 𝑥 2 𝜇 1 𝜇 25 384 2 1 superscript 𝑥 3 Big-O 1 superscript 𝑥 5 {\displaystyle{\displaystyle\phi_{\nu}\left(x\right)=-\frac{x}{\sqrt{2}}-\left% (\frac{1}{2}\nu+\frac{1}{8}\right)\pi-\frac{\mu-1}{8\sqrt{2}}\frac{1}{x}+\frac% {\mu-1}{16}\frac{1}{x^{2}}+\frac{(\mu-1)(\mu-25)}{384\sqrt{2}}\frac{1}{x^{3}}+% O\left(\frac{1}{x^{5}}\right).}}
    0 references
    DLMF:10.68.E21
    0 references
    O ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    C2.S1.E3.m2aedec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2amdec
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    ϕ ν ( x ) phase-Bessel-Phi 𝜈 𝑥 {\displaystyle{\displaystyle\phi_{\NVar{\nu}}\left(\NVar{x}\right)}}
    C10.S18.E3.m2addec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C10.S1.XMD4.m1rdec
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    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C10.S1.XMD7.m1qdec
    0 references