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An explicit expression is found, using the Poisson sum formula.
An approximate closed-form solution is obtained by applying the Euler Maclaurin sum formula.
The Euler Maclaurin sum formula is applied to the infinite series of images in the Green function for acoustic wave propagation between two perfectly reflecting parallel plates.
Such balancing requires a sum formula for biomass.
Sum formula Consists of the elements contributing to a compound and the number of their occurrences 'C9H8O4'C9H8O4
Note that Theorem 5.2 can be also obtained from the algebraic alternating sum formula applied to sequence (5.4).
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Entity class ChemSpider Chemlist IUPAC (391) 0.08 0.21 PART (92) 0.00 0.04 SUM (49) 0.25 0.29 TRIV (414) 0.45 0.80 ABB (161) 0.01 0.22 FAM (99) 0.02 0.19 IUPAC: multiword systematic names, PART: partial chemical names, SUM: sum formulas, TRIV: trivial names (including single word IUPAC names), ABB: abbreviations, FAM: chemical family names.
Thus from the finite sum formulae, we can get Equation 3: (3A).
Improved the precision of the Chemical Formula grammar (Table 1) by limiting sum formulae to just those with more than two digits, e.g. CDK2, CaCo, HeLa are no longer recognized as sum formulae.
For the calculation of sum formulae, the monoisotopic mass averaged from at least three scans has been used (resolution 10000, external calibration using sodium TFA ions clusters immediately prior to analysis).
Several filters can be activated to reduce the number of computed sum formulas.
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