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DLMF:10.68.E18 - MaRDI portal

DLMF:10.68.E18 (Q4585)

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DLMF:10.68.E18
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    Statements

    DLMF defining formula
    θ 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-Theta 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\theta_{\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
    Symbols used
    order not exceeding
    DLMF defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ajdec
    0 references
    phase of Bessel functions
    DLMF defining formula
    θ ν ⁡ ( x ) phase-Bessel-Theta 𝜈 𝑥 {\displaystyle{\displaystyle\theta_{\NVar{\nu}}\left(\NVar{x}\right)}}
    xml-id
    C10.S18.E3.m1akdec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1odec
    0 references
    complex parameter
    DLMF defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1ndec
    0 references

    Identifiers

     
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