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Formula:8972

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Digital Library of Mathematical Functions ID 28.8.E12

Q m ⁢ ( x ) ∼ sin ⁡ x cos 2 ⁡ x ⁢ ( 1 2 5 ⁢ h ⁢ ( s 2 + 3 ) + 1 2 9 ⁢ h 2 ⁢ ( s 3 + 3 ⁢ s + 4 ⁢ s 3 + 44 ⁢ s cos 2 ⁡ x ) ) + ⋯ . asymptotic-expansion subscript 𝑄 𝑚 𝑥 𝑥 2 𝑥 1 superscript 2 5 ℎ superscript 𝑠 2 3 1 superscript 2 9 superscript ℎ 2 superscript 𝑠 3 3 𝑠 4 superscript 𝑠 3 44 𝑠 2 𝑥 ⋯ {\displaystyle{\displaystyle Q_{m}(x)\sim\dfrac{\sin x}{{\cos^{2}}x}\left(% \dfrac{1}{2^{5}h}(s^{2}+3)+\dfrac{1}{2^{9}h^{2}}\left(s^{3}+3s+\dfrac{4s^{3}+4% 4s}{{\cos^{2}}x}\right)\right)+\cdots.}}


Constraint(s)

Symbols List

  • ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}} :
  • cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}} : cosine function
  • sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}} : sine function
  • m 𝑚 {\displaystyle{\displaystyle m}} : integer
  • h ℎ {\displaystyle{\displaystyle h}} : parameter
  • x 𝑥 {\displaystyle{\displaystyle x}} : real variable
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