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Formula:963

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Digital Library of Mathematical Functions ID 2.10.E5

R m ⁢ ( n ) = ∫ n ∞ B ~ 2 ⁢ m ⁡ ( x ) - B 2 ⁢ m 2 ⁢ m ⁢ ( 2 ⁢ m - 1 ) ⁢ x 2 ⁢ m - 1 ⁢ d x . subscript 𝑅 𝑚 𝑛 superscript subscript 𝑛 periodic-Bernoulli-polynomial-B 2 𝑚 𝑥 Bernoulli-number-B 2 𝑚 2 𝑚 2 𝑚 1 superscript 𝑥 2 𝑚 1 𝑥 {\displaystyle{\displaystyle R_{m}(n)=\int_{n}^{\infty}\frac{\widetilde{B}_{2m% }\left(x\right)-B_{2m}}{2m(2m-1)x^{2m-1}}\mathrm{d}x.}}


Constraint(s)

Symbols List

  • B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}} :
  • d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}} : differential of x
  • ∫ {\displaystyle{\displaystyle\int}} : integral
  • B ~ n ⁡ ( x ) periodic-Bernoulli-polynomial-B 𝑛 𝑥 {\displaystyle{\displaystyle\widetilde{B}_{\NVar{n}}\left(\NVar{x}\right)}} :
  • m 𝑚 {\displaystyle{\displaystyle m}} : integer
  • n 𝑛 {\displaystyle{\displaystyle n}} : integer
  • R m ⁢ ( n ) subscript 𝑅 𝑚 𝑛 {\displaystyle{\displaystyle R_{m}(n)}} : remainder
  •  Edit this on Wikidata

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This page was last edited on 3 March 2024, at 01:35.
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