Abramowitz and Stegun (1964) tabulates: ,
, 20D (p. 811); , , 9D (p. 1005); ,
,
, , 6D (p. 1006).
Here denotes Clausen’s integral, given by the right-hand side of (25.12.9).
…
►In 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.
…
►Because 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)).
…
…
►All terms on the right-hand sides are nonnegative when , , or , respectively.
…
►The 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).
…
►The sign on the right-hand side of (19.25.35) will change whenever one crosses a curve on which , for some .
…
►The sign on the right-hand side of (19.25.40) will change whenever one crosses a curve on which , for some .
…
…
►where is the unit vector normal to and whose direction is determined by the right-hand rule; see Figure 1.6.1.
►►►Figure 1.6.1: Vector notation.
Right-hand rule for cross products.
Magnify
…
…
►at every point at which has both a left-hand derivative (that is, (1.4.4) applies when ) and a right-hand derivative (that is, (1.4.4) applies when ).
…
…