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Goodwill and Other Identifiable Intangible Assets, Net (Details) - USD ($) $ in Thousands | 3 Months Ended | 6 Months Ended |
--- | --- | --- | ---
Mar. 31, 2021 | Mar. 31, 2020 | Mar. 31, 2021 | Mar. 31, 2020 | Sep. 30, 2020
Finite-Lived Intangible Assets [Line Items] |  |  |  |  |
Gross carrying amount | $ 226,029 |  | $ 226,029 |  | $ 225,059
Accumulated amortization | (112,487) |  | (112,487) |  | (103,811)
Net | 113,542 |  | 113,542 |  | 121,248
Amortization expense |  |  | 7,888 | $ 6,564 |
Purchased and Core Technology |  |  |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |  |  |
Gross carrying amount | 76,517 |  | 76,517 |  | 76,011
Accumulated amortization | (58,133) |  | (58,133) |  | (55,482)
Net | 18,384 |  | 18,384 |  | 20,529
License Agreements |  |  |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |  |  |
Gross carrying amount | 112 |  | 112 |  | 112
Accumulated amortization | (112) |  | (112) |  | (112)
Net | 0 |  | 0 |  | 0
Patents and Trademarks |  |  |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |  |  |
Gross carrying amount | 23,007 |  | 23,007 |  | 22,836
Accumulated amortization | (14,386) |  | (14,386) |  | (13,535)
Net | 8,621 |  | 8,621 |  | 9,301
Customer Relationships |  |  |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |  |  |
Gross carrying amount | 125,793 |  | 125,793 |  | 125,500
Accumulated amortization | (39,376) |  | (39,376) |  | (34,232)
Net | 86,417 |  | 86,417 |  | 91,268
Non-compete Agreements |  |  |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |  |  |
Gross carrying amount | 600 |  | 600 |  | 600
Accumulated amortization | (480) |  | (480) |  | (450)
Net | 120 |  | 120 |  | $ 150
Cost of Sales and General and Administrative Expense |  |  |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |  |  |
Amortization expense | $ 3,900 | $ 4,100 | $ 7,900 | $ 6,600 |

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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=121586364&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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