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Goodwill and Intangible Assets, Net (Tables) | 12 Months Ended
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Sep. 30, 2020
Goodwill and Intangible Assets Disclosure [Abstract] |
Details of Total Goodwill | The following table presents details of the Company’s total goodwill:
As of September 30, 2018 |  | $ | 2,444,895 |
Goodwill resulting from acquisitions(1) |  |  | 17,484 |
Other |  |  | 456 |
As of September 30, 2019 |  | $ | 2,462,835 |
Goodwill resulting from acquisitions(2) |  |  | 118,628 |
Other |  |  | (2,818 | )
As of September 30, 2020 |  | $ | 2,578,645 |
(1) | Mainly relates to the acquisition of TTS. In allocating the total purchase price for T TS , based on estimated fair values, the Company recorded $8,218 of goodwill, $29,500 of customer relationships to be amortized over approximately six years, $2,100 of core technology to be amortized over approximately six years and $1,300 of trade mark to be amortized over four years.
(2) | Mainly relates to the acquisition of Openet. In allocating the total preliminary purchase price for Openet, based on estimated fair values, the Company recorded $102,898 of goodwill, $40,409 of customer relationships to be amortized over approximately eight years, $53,614 of core technology to be amortized over approximately five years and $2,594 of trade mark to be amortized over two years.
Details Regarding Total Definite-Lived Purchased Intangible Assets | The following table presents details regarding the Company’s total definite-lived purchased intangible assets:
|  | Gross |  |  | Accumulated Amortization |  |  | Net |
September 30, 2020 |  |  |  |  |  |  |  |  |  |  |  |
Core technology |  | $ | 896,814 |  |  | $ | (735,534 | ) |  | $ | 161,280 |
Customer relationships |  |  | 642,575 |  |  |  | (517,670 | ) |  |  | 124,905 |
Other |  |  | 47,540 |  |  |  | (37,391 | ) |  |  | 10,149 |
Total |  | $ | 1,586,929 |  |  | $ | (1,290,595 | ) |  | $ | 296,334 |
September 30, 2019 |  |  |  |  |  |  |  |  |  |  |  |
Core technology |  | $ | 775,479 |  |  | $ | (690,961 | ) |  | $ | 84,518 |
Customer relationships |  |  | 594,555 |  |  |  | (483,313 | ) |  |  | 111,242 |
Other |  |  | 44,946 |  |  |  | (35,544 | ) |  |  | 9,402 |
Total |  | $ | 1,414,980 |  |  | $ | (1,209,818 | ) |  | $ | 205,162 |
Amortization Expense on Definite-Lived Intangible Assets | The estimated future amortization expense of def i nite-lived purchased intangible assets as of September 30, 2020 is as follows:
|  | Amount |
Fiscal year: |  |  |  |
2021 |  | $ | 78,345 |
2022 |  |  | 63,819 |
2023 |  |  | 46,672 |
2024 |  |  | 38,954 |
2025 |  |  | 34,534 |
Thereafter |  |  | 34,010 |
Total |  | $ | 296,334 |

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