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Formula:3912

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Digital Library of Mathematical Functions ID 10.18.E21

ϕ ν ⁡ ( x ) ∼ x - ( 1 2 ⁢ ν - 1 4 ) ⁢ π + μ + 3 2 ⁢ ( 4 ⁢ x ) + μ 2 + 46 ⁢ μ - 63 6 ⁢ ( 4 ⁢ x ) 3 + μ 3 + 185 ⁢ μ 2 - 2053 ⁢ μ + 1899 5 ⁢ ( 4 ⁢ x ) 5 + ⋯ . asymptotic-expansion phase-Bessel-Phi 𝜈 𝑥 𝑥 1 2 𝜈 1 4 𝜋 𝜇 3 2 4 𝑥 superscript 𝜇 2 46 𝜇 63 6 superscript 4 𝑥 3 superscript 𝜇 3 185 superscript 𝜇 2 2053 𝜇 1899 5 superscript 4 𝑥 5 ⋯ {\displaystyle{\displaystyle\phi_{\nu}\left(x\right)\sim x-\left(\frac{1}{2}% \nu-\frac{1}{4}\right)\pi+\frac{\mu+3}{2(4x)}+\frac{\mu^{2}+46\mu-63}{6(4x)^{3% }}+\frac{\mu^{3}+185\mu^{2}-2053\mu+1899}{5(4x)^{5}}+\cdots.}}


Constraint(s)

Symbols List

  • ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}} :
  • π {\displaystyle{\displaystyle\pi}} : the ratio of the circumference of a circle to its diameter
  • ϕ ν ⁡ ( x ) phase-Bessel-Phi 𝜈 𝑥 {\displaystyle{\displaystyle\phi_{\NVar{\nu}}\left(\NVar{x}\right)}} : phase of derivatives of Bessel functions
  • x 𝑥 {\displaystyle{\displaystyle x}} : real variable
  • ν 𝜈 {\displaystyle{\displaystyle\nu}} : complex parameter
  •  Edit this on Wikidata

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