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Goodwill and Intangible Assets (Tables) | 3 Months Ended
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Dec. 31, 2022
Goodwill and Intangible Assets Disclosure [Abstract] |
Schedule of Goodwill and Acquired Intangible Assets | Goodwill and acquired intangible assets consisted of the following:
(in thousands) |  | December 31, 2022 |  |  | September 30, 2022 |
|  | Gross Carrying Amount |  |  | Accumulated Amortization |  |  | Net Book Value |  |  | Gross Carrying Amount |  |  | Accumulated Amortization |  |  | Net Book Value |
Goodwill (not amortized) |  |  |  |  |  |  |  | $ | 2,388,589 |  |  |  |  |  |  |  |  | $ | 2,353,654 |
Intangible assets with finite lives (amortized): |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Purchased software |  | $ | 508,840 |  |  | $ | 366,149 |  |  | $ | 142,691 |  |  | $ | 502,859 |  |  | $ | 355,857 |  |  | $ | 147,002 |
Capitalized software |  |  | 22,877 |  |  |  | 22,877 |  |  |  | — |  |  |  | 22,877 |  |  |  | 22,877 |  |  |  | — |
Customer lists and relationships |  |  | 605,366 |  |  |  | 384,198 |  |  |  | 221,168 |  |  |  | 594,970 |  |  |  | 369,390 |  |  |  | 225,580 |
Trademarks and trade names |  |  | 27,911 |  |  |  | 17,933 |  |  |  | 9,978 |  |  |  | 27,546 |  |  |  | 17,410 |  |  |  | 10,136 |
Other |  |  | 3,885 |  |  |  | 3,885 |  |  |  | — |  |  |  | 3,766 |  |  |  | 3,766 |  |  |  | — |
Total intangible assets with finite lives |  | $ | 1,168,879 |  |  | $ | 795,042 |  |  | $ | 373,837 |  |  | $ | 1,152,018 |  |  | $ | 769,300 |  |  | $ | 382,718 |
Total goodwill and acquired intangible assets |  |  |  |  |  |  |  | $ | 2,762,426 |  |  |  |  |  |  |  |  | $ | 2,736,372 |
Schedule of Changes in Goodwill by Reportable Segments | Changes in goodwill presented by reportable segments were as follows:
(in thousands) |  | Software Products |  |  | Professional Services |  |  | Total |
Balance, October 1, 2022 |  | $ | 2,344,019 |  |  | $ | 9,635 |  |  | $ | 2,353,654 |
Foreign currency translation adjustment |  |  | 34,793 |  |  |  | 142 |  |  |  | 34,935 |
Balance, December 31, 2022 |  | $ | 2,378,812 |  |  | $ | 9,777 |  |  | $ | 2,388,589 |
Schedule of Aggregate Amortization Expense for Intangible Assets with Finite Lives | The aggregate amortization expense for intangible assets with finite lives is classified in our Consolidated Statements of Operations as follows:
(in thousands) |  | Three months ended |
|  | December 31, 2022 |  |  | December 31, 2021 |
Amortization of acquired intangible assets |  | $ | 8,026 |  |  | $ | 8,484 |
Cost of license revenue |  |  | 6,142 |  |  |  | 6,493 |
Total amortization expense |  | $ | 14,168 |  |  | $ | 14,977 |

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