Vector Representation of Non-Harmonic Alternating Currents
نویسندگان
چکیده
منابع مشابه
Mod p structure of alternating and non-alternating multiple harmonic sums
The well-known Wolstenholme’s Theorem says that for every prime p > 3 the (p−1)-st partial sum of the harmonic series is congruent to 0 modulo p2. If one replaces the harmonic series by ∑ k≥1 1/n for k even, then the modulus has to be changed from p2 to just p. One may consider generalizations of this to multiple harmonic sums (MHS) and alternating multiple harmonic sums (AMHS) which are partia...
متن کاملCongruences of Alternating Multiple Harmonic Sums
By convention we set H(s;n) = 0 any n < d. We call l(s) := d and |s| := ∑d i=1 |si| its depth and weight, respectively. We point out that l(s) is sometimes called length in the literature. When every si is positive we recover the multiple harmonic sums (MHS for short) whose congruence properties are studied in [9, 10, 17, 18]. There is another “non-strict” version of the AMHS defined as follows...
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We show that for any prime prime p = 2 p−1 k=1 (−1) k k − 1 2 k ≡ − (p−1)/2 k=1 1 k (mod p 3) by expressing the l.h.s. as a combination of alternating multiple harmonic sums.
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We show that for any prime prime p = 2, p−1 k=1 (−1) k k − 1 2 k ≡ − (p−1)/2 k=1 1 k (mod p 3) by expressing the left-hand side as a combination of alternating multiple harmonic sums.
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ژورنال
عنوان ژورنال: Physical Review (Series I)
سال: 1909
ISSN: 1536-6065
DOI: 10.1103/physrevseriesi.29.409