Fokker block: Difference between revisions

Inthar (talk | contribs)
Inthar (talk | contribs)
m First definition of a Fokker block: Cut out more redundancy.
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<math>S[i] = \bigg\lfloor \dfrac{e_1 i + a_1}{P} \bigg\rfloor t_1 + \cdots + \bigg\lfloor \dfrac{e_n i + a_n}{P} \bigg\rfloor t_n.</math>
<math>S[i] = \bigg\lfloor \dfrac{e_1 i + a_1}{P} \bigg\rfloor t_1 + \cdots + \bigg\lfloor \dfrac{e_n i + a_n}{P} \bigg\rfloor t_n.</math>


Here &lfloor;''x''&rfloor; is the [[Wikipedia: Floor and ceiling functions|floor function]], the [[Wikipedia: Quasiperiodic function|quasiperiodic function]] returning the largest integer less than or equal to ''x''. When ''i'' = 0, since ''a''<sub>''k''</sub> &lt; P each term is 0 and so S[0] = 0. Since for integer ''j'', &lfloor;''x'' + ''j''&rfloor; = &lfloor;''x''&rfloor; + ''j'', we have
Here &lfloor;''x''&rfloor; is the [[Wikipedia: Floor and ceiling functions|floor function]], which returns the largest integer less than or equal to ''x''. When ''i'' = 0, since ''a''<sub>''k''</sub> &lt; P each term is 0 and so S[0] = 0. Since for integer ''j'', &lfloor;''x'' + ''j''&rfloor; = &lfloor;''x''&rfloor; + ''j'', we have


<math>S[i+P] = S[i] + e_1 t_1 + e_2 t_2 + … + e_n t_n = S[i] + 1</math>
<math>S[i+P] = S[i] + e_1 t_1 + e_2 t_2 + … + e_n t_n = S[i] + 1</math>