Below are the formal and polite equivalents (synonyms) of 'ask for' which you can use in your business or professional pieces of writing.
The below synonyms are used when you want somebody to do something or to give you an object/thing. You wouldn't use these if you are asking for information on something or somebody. For this, see the synonyms in 'ask about'.
This is used when you are 'asking for' something which is free.
'Last week I requested a copy of the sales report for last year.'
This is a different way of saying 'request'.
'Last week I made a request for a meeting with the sales director.'
When you have to pay for the thing you are 'asking for', you should use 'order'.
'I would like to order a copy of the new photoshop software.'