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Goodwill and Intangible Assets (Tables)
 6 Months Ended
Jun. 30, 2021
Goodwill and Intangible Assets Disclosure [Abstract]  
Intangible Assets (Indefinite-Lived)
Intangible assets are classified as follows:
 June 30, 2021December 31, 2020
(in thousands)Gross
Carrying
Amount		Accumulated
Amortization		Gross
Carrying
Amount		Accumulated
Amortization
Finite-lived intangible assets:
Developed software and core technologies
$890,397 $(396,417)$859,620 $(370,338)
Customer lists and contract backlog 286,732 (142,392)288,085 (136,093)
Trade names 176,262 (125,541)175,626 (122,392)
Total$1,353,391 $(664,350)$1,323,331 $(628,823)
Indefinite-lived intangible asset:
Trade name$357 $357 
Intangible Assets (Finite-Lived)
Intangible assets are classified as follows:
 June 30, 2021December 31, 2020
(in thousands)Gross
Carrying
Amount		Accumulated
Amortization		Gross
Carrying
Amount		Accumulated
Amortization
Finite-lived intangible assets:
Developed software and core technologies
$890,397 $(396,417)$859,620 $(370,338)
Customer lists and contract backlog 286,732 (142,392)288,085 (136,093)
Trade names 176,262 (125,541)175,626 (122,392)
Total$1,353,391 $(664,350)$1,323,331 $(628,823)
Indefinite-lived intangible asset:
Trade name$357 $357 
Estimated Future Amortization Expense for Intangible Assets
As of June 30, 2021, estimated future amortization expense for the intangible assets reflected above was as follows:
(in thousands) 
Remainder of 2021$36,684 
202278,527 
202380,665 
202480,069 
202577,767 
202675,567 
Thereafter259,762 
Total intangible assets subject to amortization689,041 
Indefinite-lived trade name357 
Other intangible assets, net$689,398 
Changes in Goodwill
The changes in goodwill during the six months ended June 30, 2021 and 2020 were as follows:
(in thousands)20212020
Beginning balance – January 1$3,038,306 $2,413,280 
Acquisitions and adjustments(1)
78,610 69,330 
Currency translation(6,180)(8,311)
Ending balance – June 30$3,110,736 $2,474,299 
(1) In accordance with the accounting for business combinations, we recorded adjustments to goodwill for the effect of changes in the provisional fair values of the assets acquired and liabilities assumed during the measurement period (up to one year from the acquisition date) as we obtained new information about facts and circumstances that existed as of the acquisition date that, if known, would have affected the measurement of the amounts recognized as of that date.