Question: question about fractional form / evaluating cfrac with option 'quotient'

Where can I find a description for the various variants of numtheory:-cfrac, which goes more into details than the online help? For example one can guess how an approximating sum can be obtained from numtheory:-cfrac((a+x)^k, x, 7, 'diag', 'simregular', 'quotients'); but I prefer to cross-check against a confirmed formula instead of guessing. If somebody would be so kind to point me to some source to look at ... or even knows it already ...: how does one evaluate the above list to get a value? -- edited to add: I mean a way which can be compiled and without running through showstat(nthnumer); showstat(nthdenom); showstat('numtheory:-nthnumer_aux');
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