with corresponding equations for and obtained by permuting . Also,
with and obtained by permuting , , and . (Note that .) Equivalent forms of (19.26.2) are given by
where , , , and
Equivalent forms of (19.26.11) are given by
where for , except that can be 0, and
If , then . For example,
An equivalent version for is
either upper or lower signs being taken throughout.
The equations inverse to and the two other equations obtained by permuting (see (19.26.19)) are
and two similar equations obtained by exchanging with (and with ), or with (and with ).
Equivalent forms are given by (19.22.22). Also,