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WebMay 16, 2024 · The claim is that Hn is not an integer for all n ≥ 2 . Aiming for a contradiction, suppose otherwise: (P): ∃m ∈ N: Hm ∈ Z. By the definition of the harmonic numbers : … WebE N O M Z V E Z W Y X J B P H R N F I R V X X T J T O N H K Z G N P L W J B T P D V X S Y Z E F V F L D V K Y P X H F R S C C K. 5. THERE’S SOMETHING VERY … When seeking to approximate H x for a complex number x, it is effective to first compute H m for some large integer m. Use that as an approximation for the value of H m + x . Then use the recursion relation H n = H n −1 + 1/ n backwards m times, to unwind it to an approximation for H x . See more In mathematics, the n-th harmonic number is the sum of the reciprocals of the first n natural numbers: Starting from n = 1, the sequence of harmonic numbers begins: Harmonic numbers … See more A generating function for the harmonic numbers is See more Generalized harmonic numbers The nth generalized harmonic number of order m is given by (In some sources, … See more • Watterson estimator • Tajima's D • Coupon collector's problem See more The harmonic numbers have several interesting arithmetic properties. It is well-known that $${\textstyle H_{n}}$$ is an integer See more The formulae given above, The Taylor series for the harmonic numbers is Approximation using the Taylor series expansion See more • Weisstein, Eric W. "Harmonic Number". MathWorld. This article incorporates material from Harmonic number on See more heitman uk