[JBKProductions]

Let's say I have a function of some parameters where we can assume x, y and z are functions and can be written as a power series in h. How can i substitute this power series into my function in mathematica? I hope this is clear enough, if not let me know. Thanks.
EDIT: Also is there a way to remove second order terms and higher from the function?

[DrSheldonCooper]

not really sure i`ve got your jist but, i`ll give it a go (forgive me if i`m wrong)

do you want to have expressions (power series of order one?) in h, for each of x, y, and z which are expressions in h?

and to sub these into F?

[DrSheldonCooper]

i`ve just messed around with these, where x,y, and z have thier own power series in h,

and a funstion is defined as functn= (EDIT: you can call it what you like!)

i don`t really know if this is what you`re after, but it demonstates my thinking - again, my apologies if it`s not what you`re after!

x = Series[Exp[h], {h, 0, 1}] // Normal (output = 1+h)

y = Series[Sin[h], {h, 0, 2}] // Normal (output =h)

z = Series[Log[h], {h, 0, 3}] // Normal (output = Log[h])

so the function:

functn = Function[{u, v, w}, u^2 + v^4 + w][x, y, z] (this is just my example) (output h^4 + (1 + h)^2 + Log[h])

this is a pure function, though, the disadvantage being, it`s not like F[x_], say, where you can say F[2] or F'[2]

again - apologies if this isn`t what your looking for.

[JBKProductions]

(Original post by DrSheldonCooper)
not really sure i`ve got your jist but, i`ll give it a go (forgive me if i`m wrong)

do you want to have expressions (power series of order one?) in h, for each of x, y, and z which are expressions in h?

and to sub these into F?

Yep, this is what I'm after. I haven't read your other reply yet, so going to do that now!

[DrSheldonCooper]

there`s probably a shorter way - but i can`t think of it!

again - in the above definitions of x,y,z, first of all i dont use the??Normal, to be sure of what order the thing "would be" - then if it only has 2 orders in it you can leave the {h,0,1 or 2 or3} alone and use//Normal

[JBKProductions]

(Original post by DrSheldonCooper)

functn = Function[{u, v, w}, u^2 + v^4 + w][x, y, z] (this is just my example) (output h^4 + (1 + h)^2 + Log[h])

Hi, just read it and this output is what you get at the end? Is there a way to remove second order terms and higher on this function you have? I want just functn to have only constant terms and h terms.

[DrSheldonCooper]

i`ve not used this at all, but if you go to the documentation centre, and type the word: drop, drop tells you how to get rid of certain elements of lists and expressions. Beyond that i`m not too sure - hope you find out!

(p.s. be sure to expand/simplify functn before you try drop)

good luck!