# Create list of values with arbitrary index and the use it in a function

I have the following generating functions:

$$l_{2i-1}=l_{1}-(i-2)(w+s)$$ with $$i\geq 2$$ and $$l_{2i}=l_{2}-(i-1)(w+s)$$ with $$i\geq 2$$, so the first one is for odd index and the second for even index. Then I need to use the two for a function, let´s say a sum, So i'm going to need $$l_{1},l_2,l_3,...$$ etc but these are generated from the two different functions, so how can I call the $$l_{odd}$$ using the first function and $$l_{even}$$ using the second function in the same sum ?

I tried simply defining my first function like f[2*i_-1] but it doesn´t work :(

Many thanks,

One way is to use OddQ and EvenQ. For example:

m[x_] := x^2 /; OddQ[x]
m[x_] := 5 x^3 /; EvenQ[x]


defines m differently for odd and even arguments. For your f, maybe something like

f[x_] := l1 - (x - 2) (w + s) /; OddQ[x]
f[x_] := l2 - (x - 1) (w + s) /; EvenQ[x]

• g[x_?OddQ] := l1 - (x - 2) (w + s);g[x_?EvenQ] := l2 - (x - 1) (w + s); is also an alternative and maybe even a bit faster. Sep 27 '18 at 22:08
• To actually match the mathematical definition given by the OP, you need to do g[x_?OddQ] := l1 - Quotient[x - 3, 2] (w + s) and g[x_?EvenQ] := l2 - Quotient[x - 2, 2] (w + s). Sep 28 '18 at 0:12
• But is any way to add the condition of Odd or Even to the subindex ? Because the subindex "i" in the two functions take Odd and Even values starting from 2, but because of the definition (2i-1) generate the Even indexes and (2i) the odd indexes, Sep 28 '18 at 19:47