Trade accounts receivable - Trade accounts receivable, less allowance for doubtful accounts (Details) - EUR (€)	12 Months Ended
	Dec. 31, 2017	Mar. 31, 2019	Dec. 31, 2018
Trade accounts receivable [Line Items]
Trade accounts receivable		€ 3,980,307,000	€ 3,455,721,000
finance lease receivables		44,037,000	28,726,000
less allowance for doubtful accounts		123,416,000	118,015,000
Trade accounts receivable, net		3,856,891,000	3,337,706,000
Collection period for trade accounts receivable	1 year
Trade accounts receivable included in other non-current assets		120,479,000	120,668,000
other receivables		79,627,000
Credit impaired trade AR [Member]
Trade accounts receivable [Line Items]
Trade accounts receivable		387,850,000	325,240,000
less allowance for doubtful accounts		87,056,000	(85,775,000)
Trade accounts receivable, net		€ 300,794,000	€ 239,465,000