sum rule
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1: 34.7 Basic Properties: Symbol
2: 34.5 Basic Properties: Symbol
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►Equations (34.5.15) and (34.5.16) are the sum rules.
They constitute addition theorems for the symbol.
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3: Bibliography R
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Finite-sum rules for Macdonald’s functions and Hankel’s symbols.
Integral Transform. Spec. Funct. 10 (2), pp. 115–124.
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4: 1.2 Elementary Algebra
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►This is the row times column rule.
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►If then, depending on , there is either no solution or there are infinitely many solutions, being the sum of a particular solution of (1.2.61) and any solution of .
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►Nonzero vectors are linearly independent if implies that all coefficients are zero.
…The sum of all multiplicities is .
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►Thus is the sum of the (counted according to their multiplicities) eigenvalues of .
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5: 29.20 Methods of Computation
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►A second approach is to solve the continued-fraction equations typified by (29.3.10) by Newton’s rule or other iterative methods; see §3.8.
…The Fourier series may be summed using Clenshaw’s algorithm; see §3.11(ii).
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6: 3.5 Quadrature
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§3.5(i) Trapezoidal Rules
… ►The composite trapezoidal rule is … ►§3.5(ii) Simpson’s Rule
… ►§3.5(iv) Interpolatory Quadrature Rules
… ► …7: 17.2 Calculus
8: 1.4 Calculus of One Variable
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Chain Rule
… ►where the sum is over all nonnegative integers that satisfy , and . ►L’Hôpital’s Rule
… ►Definite integrals over the Stieltjes measure could represent a sum, an integral, or a combination of the two. Let , , . …9: 1.6 Vectors and Vector-Valued Functions
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►where is the unit vector normal to and whose direction is determined by the right-hand rule; see Figure 1.6.1.
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►In almost all cases of repeated suffices, we can suppress the summation notation entirely, if it is understood that an implicit sum is to be taken over any repeated suffix.
Thus pairs of indefinite suffices in an expression are resolved by being summed over (or “traced” over).
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10: 3.3 Interpolation
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3.3.1
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3.3.3_2
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3.3.4
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►and compute an approximation to by using Newton’s rule (§3.8(ii)) with starting value .
…Then by using in Newton’s interpolation formula, evaluating and recomputing , another application of Newton’s rule with starting value gives the approximation , with 8 correct digits.
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