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CRC Standard Mathematical Tables (also CRC Standard Mathematical Tables and Formulas or SMTF) is a comprehensive one-volume handbook containing a fundamental working knowledge of mathematics and tables of formulas.
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
This is a list of common chemical compounds with chemical formulae and CAS numbers, indexed by formula. This complements alternative listing at list of inorganic compounds. There is no complete list of chemical compounds since by nature the list would be infinite.
A molecular formula enumerates the number of atoms to reflect those in the molecule, so that the molecular formula for glucose is C 6 H 12 O 6 rather than the glucose empirical formula, which is CH 2 O. Except for the very simple substances, molecular chemical formulas generally lack needed structural information, and might even be ambiguous in ...
In physics, there are equations in every field to relate physical quantities to each other and perform calculations. Entire handbooks of equations can only summarize most of the full subject, else are highly specialized within a certain field.
The formula Na 2 SO 3 denotes that the cation is sodium, or Na +, and that the anion is the sulfite ion (SO 2− 3). Therefore, this compound is named sodium sulfite. If the given formula is Ca(OH) 2, it can be seen that OH − is the hydroxide ion.
Integration using Euler's formula – Use of complex numbers to evaluate integrals; Liouville's theorem (differential algebra) – Says when antiderivatives of elementary functions can be expressed as elementary functions; List of limits; List of mathematical identities; List of mathematical series
More formulas of this nature can be given, as explained by Ramanujan's theory of elliptic functions to alternative bases. Perhaps the most notable hypergeometric inversions are the following two examples, involving the Ramanujan tau function τ {\displaystyle \tau } and the Fourier coefficients j {\displaystyle \mathrm {j} } of the J-invariant ...