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May 24th, 2019, 06:49 AM   #1
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Functions in function - synthesis of a general form

Hi All,

I've one question related to a function, which can be defined by using other functions. Let we say, that such situation can be defined as follows:

$\displaystyle f_{0}(q)= \frac{a_{0}+c \cdot f_{1}(q)}{c \cdot a_{0}+ f_{1}(q)} $

$\displaystyle f_{1}(q)= \frac{a_{1}+c \cdot f_{2}(q)}{c \cdot a_{1}+ f_{2}(q)} $

$\displaystyle f_{2}(q)= \frac{a_{2}+c \cdot f_{3}(q)}{c \cdot a_{2}+ f_{3}(q)} $ ... and so on.

As you can see, function f0(q) is constructed on fn(x) 's where n-index is defining number of functions placed inside.

Now:
I want to synthesize general form of equation which will define such function f0(q) in relation to the number of functions fn(q) number. Firstly, I thought that recursion will be good to solve this problem, however function f0(q) it doesn't "call itself". I believe, that there are some methods which can be used to bring solution in this case. Can you suggest some of them ?

Best Regards,
E.
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