Selected Quarterly Financial Data (Unaudited) (Details) - USD ($) $ / shares in Units, $ in Thousands	3 Months Ended								12 Months Ended
	Sep. 30, 2017	Jun. 30, 2017	Mar. 31, 2017	Dec. 31, 2016	Sep. 30, 2016	Jun. 30, 2016	Mar. 31, 2016	Dec. 31, 2015	Sep. 30, 2017	Sep. 30, 2016	Sep. 30, 2015
Quarterly Financial Information Disclosure [Abstract]
Total Income	$ 142,240	$ 137,716	$ 136,198	$ 132,764	$ 132,872	$ 133,735	$ 135,063	$ 135,124	$ 548,918	$ 536,793	$ 530,553
Interest expense	29,808	29,101	28,471	29,612	30,056	29,495	28,738	28,255	116,992	116,544	117,072
Net interest income	112,432	108,615	107,727	103,152	102,816	104,240	106,325	106,869	431,926	420,249	413,481
Provision (release) for loan losses	(500)	0	(1,600)	0	(3,100)	(1,650)	(1,500)	0	(2,100)	(6,250)	(11,162)
Other operating income (including REO gain (loss), net)	16,686	13,798	10,931	12,294	14,830	15,573	14,623	12,055
Other operating expense	62,649	57,062	57,467	54,341	55,407	56,305	59,226	64,509	231,519	235,447	224,851
Income before income taxes	66,969	65,351	62,791	61,105	65,339	65,158	63,222	54,415	256,216	248,134	249,519
Income tax expense	20,865	21,239	20,721	19,859	21,115	22,154	21,499	19,317	82,684	84,085	89,203
NET INCOME	$ 46,104	$ 44,112	$ 42,070	$ 41,246	$ 44,224	$ 43,004	$ 41,723	$ 35,098	$ 173,532	$ 164,049	$ 160,316
Basic earnings per share (in dollars per share)	$ 0.53	$ 0.49	$ 0.47	$ 0.46	$ 0.49	$ 0.47	$ 0.45	$ 0.38	$ 1.95	$ 1.79	$ 1.68
Diluted earnings per share (in dollars per share)	0.52	0.49	0.47	0.46	0.49	0.47	0.45	0.38	1.94	1.78	1.67
Cash dividends per share (in dollars per share)	$ 0.15	$ 0.15	$ 0.40	$ 0.14	$ 0.14	$ 0.14	$ 0.14	$ 0.13	$ 0.84	$ 0.55	$ 0.54