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Formula:8909

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Digital Library of Mathematical Functions ID 28.4.E22

A m + 2 ⁢ s m ⁢ ( q ) B m + 2 ⁢ s m ⁢ ( q ) } = ( ( - 1 ) s ⁢ m ! s ! ⁢ ( m + s ) ! ⁢ ( q 4 ) s + O ⁡ ( q s + 1 ) ) ⁢ { A m m ⁢ ( q ) , B m m ⁢ ( q ) , selection subscript superscript 𝐴 𝑚 𝑚 2 𝑠 𝑞 subscript superscript 𝐵 𝑚 𝑚 2 𝑠 𝑞 superscript 1 𝑠 𝑚 𝑠 𝑚 𝑠 superscript 𝑞 4 𝑠 Big-O superscript 𝑞 𝑠 1 selection subscript superscript 𝐴 𝑚 𝑚 𝑞 subscript superscript 𝐵 𝑚 𝑚 𝑞 {\displaystyle{\displaystyle\rselection{A^{m}_{m+2s}(q)\\ B^{m}_{m+2s}(q)}=\left(\dfrac{(-1)^{s}m!}{s!(m+s)!}\left(\frac{q}{4}\right)^{s% }+O\left(q^{s+1}\right)\right)\lselection{A^{m}_{m}(q),\\ B^{m}_{m}(q),}}}


Constraint(s)

Symbols List

  • O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}} : order not exceeding
  • ! {\displaystyle{\displaystyle!}} :
  • m 𝑚 {\displaystyle{\displaystyle m}} : integer
  • q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}} : parameter
  • A m ⁢ ( q ) subscript 𝐴 𝑚 𝑞 {\displaystyle{\displaystyle A_{m}(q)}} : Fourier coefficient
  • B m ⁢ ( q ) subscript 𝐵 𝑚 𝑞 {\displaystyle{\displaystyle B_{m}(q)}} : Fourier coefficient
  •  Edit this on Wikidata

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This page was last edited on 28 January 2024, at 10:30.
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