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Intangible Assets and Goodwill (Details 3) - USD ($) $ in Thousands | 12 Months Ended
--- | ---
Dec. 31, 2019 | Dec. 31, 2018 | Dec. 31, 2017
Purchased patents |  |  |
Amortization of intangible assets | $ 17,058 | $ 29,341 | $ 41,962
Estimated future amortization expense of intangible assets |  |  |
Next Twelve Months | 18,413 |  |
Year Two | 14,411 |  |
Year Three | 7,444 |  |
Year Four | 6,740 |  |
Year Five | 5,292 |  |
Thereafter | 0 |  |
Finite-lived intangible assets | 52,300 |  |
Indefinite-lived Intangible Assets (Excluding Goodwill) | 2,600 |  |
Intangible Assets, Net (Excluding Goodwill) | 54,900 | 59,936 |
Customer contracts and contractual relationships |  |  |
Estimated future amortization expense of intangible assets |  |  |
Finite-lived intangible assets | 2,865 | 13,257 |
Existing technology |  |  |
Estimated future amortization expense of intangible assets |  |  |
Finite-lived intangible assets | $ 49,435 | $ 45,079 |
Non-competition agreements |  |  |
Identified intangible assets assumed in the acquisitions |  |  |
Useful life (in years) | 3 years | 3 years |
Estimated future amortization expense of intangible assets |  |  |
Finite-lived intangible assets | $ 0 | $ 0 |
Minimum |  |  |
Identified intangible assets assumed in the acquisitions |  |  |
Useful life (in years) | 6 months | 1 year |
Minimum | Customer contracts and contractual relationships |  |  |
Identified intangible assets assumed in the acquisitions |  |  |
Useful life (in years) | 6 months | 1 year |
Minimum | Existing technology |  |  |
Identified intangible assets assumed in the acquisitions |  |  |
Useful life (in years) | 3 years | 3 years |

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- Definition Amount of amortization expense for assets, excluding financial assets and goodwill, lacking physical substance with a life expected to be recognized after the fifth fiscal year following the latest fiscal year. Excludes interim and annual periods when interim periods are reported on a rolling approach, from latest balance sheet date. + References No definition available. + Details
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- Definition The aggregate expense charged against earnings to allocate the cost of intangible assets (nonphysical assets not used in production) in a systematic and rational manner to the periods expected to benefit from such assets. As a noncash expense, this element is added back to net income when calculating cash provided by or used in operations using the indirect method. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 230 -SubTopic 10 -Section 45 -Paragraph 28 -Subparagraph (b) -URI http://asc.fasb.org/extlink&oid=109223946&loc=d3e3602-108585 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 30 -Section 50 -Paragraph 2 -Subparagraph (a)(2) -URI http://asc.fasb.org/extlink&oid=66006027&loc=d3e16323-109275 Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 30 -Section 45 -Paragraph 2 -URI http://asc.fasb.org/extlink&oid=6388964&loc=d3e16225-109274 + Details
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