# How to create a list of undefined functions?

I have a undefined function $$\phi[i,j]$$ where $$i=0,1,...,m$$ and $$i=0,1,...,n$$.

How can I generate this list:

{$$\phi[0,0],\phi[1,0],...,\phi[m,0],\phi[0,1],\phi[1,1],...\phi[m,1],\phi[0,2],...,\phi[m,n]$$}

where I have all the iterations of $$i$$ and $$j$$ on the $$\phi$$ function?

• Try Array, for example: Flatten[Array[f, {5, 4}]] May 15, 2019 at 20:31
• Perhaps Tuples[φ[Range[0, 3], Range[0, 2]]] May 15, 2019 at 20:34

It's as straightforward as:

m = 10;
n = 10;
Flatten[Table[f[i, j], {i, 1, m}, {j, 1, n}]]

(*{f[1, 1], f[1, 2], f[1, 3], f[1, 4], f[1, 5], f[1, 6], f[1, 7],
f[1, 8], f[1, 9], f[1, 10], f[2, 1], f[2, 2], f[2, 3], f[2, 4],
f[2, 5], f[2, 6], f[2, 7], f[2, 8], f[2, 9], f[2, 10], f[3, 1],
f[3, 2], f[3, 3], f[3, 4], f[3, 5], f[3, 6], f[3, 7], f[3, 8],
f[3, 9], f[3, 10], f[4, 1], f[4, 2], f[4, 3], f[4, 4], f[4, 5],
f[4, 6], f[4, 7], f[4, 8], f[4, 9], f[4, 10], f[5, 1], f[5, 2],
f[5, 3], f[5, 4], f[5, 5], f[5, 6], f[5, 7], f[5, 8], f[5, 9],
f[5, 10], f[6, 1], f[6, 2], f[6, 3], f[6, 4], f[6, 5], f[6, 6],
f[6, 7], f[6, 8], f[6, 9], f[6, 10], f[7, 1], f[7, 2], f[7, 3],
f[7, 4], f[7, 5], f[7, 6], f[7, 7], f[7, 8], f[7, 9], f[7, 10],
f[8, 1], f[8, 2], f[8, 3], f[8, 4], f[8, 5], f[8, 6], f[8, 7],
f[8, 8], f[8, 9], f[8, 10], f[9, 1], f[9, 2], f[9, 3], f[9, 4],
f[9, 5], f[9, 6], f[9, 7], f[9, 8], f[9, 9], f[9, 10], f[10, 1],
f[10, 2], f[10, 3], f[10, 4], f[10, 5], f[10, 6], f[10, 7], f[10, 8],
f[10, 9], f[10, 10]} *)