A classic approach, known from other programming languages, in which a function calls itself:
create or replace function recursive_function (ct int, pr int)
returns table (counter int, product int)
language plpgsql
as $$
begin
return query select ct, pr;
if ct < 10 then
return query select * from recursive_function(ct+ 1, pr * (ct+ 1));
end if;
end $$;
select * from recursive_function (1, 1);
You can compare this with an iterative solution in a loop:
create or replace function loop_function ()
returns table (counter int, product int)
language plpgsql
as $$
declare
ct int;
pr int = 1;
begin
for ct in 1..10 loop
pr = ct* pr;
return query select ct, pr;
end loop;
end $$;
select * from loop_function ();
Of course, you can also put the recursive query inside an SQL function:
create or replace function recursive_query()
returns table (counter int, product int)
language sql
as $$
with recursive source as (
select 1 as counter, 1 as product
union all
select counter+ 1, product* (counter+ 1)
from source
where counter < 10
)
select counter, product
from source
$$;
select * from recursive_query();