right-hand rule for cross products
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1—10 of 351 matching pages
1: 24.19 Methods of Computation
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βΊ
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βΊIf denotes the right-hand side of (24.19.1) but with the second product taken only for , then for .
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24.19.1
βΊ
2: 16.5 Integral Representations and Integrals
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βΊ
16.5.1
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βΊIn the case the left-hand side of (16.5.1) is an entire function, and the right-hand side supplies an integral representation valid when .
In the case the right-hand side of (16.5.1) supplies the analytic continuation of the left-hand side from the open unit disk to the sector ; compare §16.2(iii).
Lastly, when the right-hand side of (16.5.1) can be regarded as the definition of the (customarily undefined) left-hand side.
In this event, the formal power-series expansion of the left-hand side (obtained from (16.2.1)) is the asymptotic expansion of the right-hand side as in the sector , where is an arbitrary small positive constant.
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3: 19.21 Connection Formulas
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βΊThe case shows that the product of the two lemniscate constants, (19.20.2) and (19.20.22), is .
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βΊ
19.21.7
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βΊ
19.21.8
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βΊ
19.21.10
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βΊBecause is completely symmetric, can be permuted on the right-hand side of (19.21.10) so that if the variables are real, thereby avoiding cancellations when is calculated from and (see §19.36(i)).
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4: 19.25 Relations to Other Functions
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βΊ
19.25.7
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βΊAll terms on the right-hand sides are nonnegative when , , or , respectively.
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βΊThe transformations in §19.7(ii) result from the symmetry and homogeneity of functions on the right-hand sides of (19.25.5), (19.25.7), and (19.25.14).
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βΊThe sign on the right-hand side of (19.25.35) will change whenever one crosses a curve on which , for some .
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βΊThe sign on the right-hand side of (19.25.40) will change whenever one crosses a curve on which , for some .
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5: 1.6 Vectors and Vector-Valued Functions
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βΊ
Dot Product (or Scalar Product)
… βΊCross Product (or Vector Product)
… βΊwhere is the unit vector normal to and whose direction is determined by the right-hand rule; see Figure 1.6.1. βΊ …6: 11.9 Lommel Functions
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11.9.4
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βΊthe right-hand side being replaced by its limiting form when is an odd negative integer.
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βΊIf either of equals an odd positive integer, then the right-hand side of (11.9.9) terminates and represents exactly.
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7: 4.24 Inverse Trigonometric Functions: Further Properties
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βΊThe above equations are interpreted in the sense that every value of the left-hand side is a value of the right-hand side and vice versa.
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8: 25.19 Tables
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βΊ
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9: 32.15 Orthogonal Polynomials
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βΊFor this result and applications see Fokas et al. (1991): in this reference, on the right-hand side of Eq.
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