Derivatives and Hedging Activities - Gains/(Losses) on Derivative Instruments in Fair Value and Cash Flow Accounting Hedging Relationships (Details) - USD ($) $ in Thousands	12 Months Ended
Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Derivative Instruments, Gain (Loss) [Line Items]
Interest income/(expense), including the effects of fair value and cash flow hedges	$ 1,165,849	$ 900,068	$ 601,592
Interest income/(expense), including the effects of fair value and cash flow hedges	(178,444)	(115,488)	$ (28,729)
Interest rate contracts \| Interest income on loans receivable \| Fair value hedging
Gain/(loss) on fair value hedging relationships:
Amounts related to interest settlements on derivatives	39,223	16,975
Recognized on derivatives	(67,785)	10,519
Recognized on hedged items	67,639	(9,775)
Net income/(expense) recognized on fair value hedges	39,077	17,719
Interest rate contracts \| Interest expense on FHLB advances \| Cash flow hedging
Gain/(loss) on cash flow hedging relationships:
Amounts related to interest settlements on derivatives	46,645	38,709
Amount of derivative gain/(loss) reclassified from AOCI into interest income/expense	0	0
Net income/(expense) recognized on cash flow hedges	$ 46,645	$ 38,709

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Amount of gain (loss) from the increase (decrease) in fair value of derivative and nonderivative instruments designated as fair value hedging instruments recognized in the income statement.

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Amount of the increase (decrease) in fair value of the hedged item in a fair value hedge recognized in the income statement.

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Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

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Aggregate net gain (loss) on all derivative instruments recognized in earnings during the period, before tax effects.

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Total amount of gain (loss) derived from fair value hedges recognized in earnings in the period.

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The aggregate interest and fee income generated by: (1) loans the Entity has positive intent and ability to hold for the foreseeable future, or until maturity or payoff, including commercial and consumer loans, whether domestic or foreign, which may consist of: (a) industrial and agricultural; (b) real estate; and (c) real estate construction loans; (d) trade financing; (e) lease financing; (f) home equity lines-of-credit; (g) automobile and other vehicle loans; and (h) credit card and other revolving-type loans and (2) loans and leases held-for-sale which may include mortgage loans, direct financing, and sales-type leases.

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Aggregate amount of interest expense on all borrowings.

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Amount, before tax, of reclassification of gain (loss) from accumulated other comprehensive income (AOCI) for derivative instrument designated and qualifying as cash flow hedge included in assessment of hedge effectiveness.

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Change In Unrealized Gain (Loss) On Cash Flow Hedging Instruments, Related To Interest Settlements

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