pathalogical "families" of geometric+algebraic series

[shaharhas]

There are phatalogical families of (infitismal) function,
Are There Example of Phatalogical Families series?
2 meaning to Family:
(1)FAMILY A = Collection of number with a rule, a series
(2)FAMILY B = Collection of families from kind A.
Thanks, in advac!!!

 

[shaharhas]

2 Question:
(1) What is your definition of patalogical function?
(2) What is the easy and in v- e-r-y simple words/definition that unambioust to formal definition patalogic functionn?
(3)CAn be relationship tyo the above function?