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Stock-Based Compensation (Tables)
 3 Months Ended
Dec. 31, 2021
Share-based Payment Arrangement [Abstract]  
Stock Based Compensation Included in Consolidated Statements of Operations The amounts included in the consolidated statements of operations related to stock-based compensation are as follows (dollars in thousands): 
 Three Months Ended December 31,
20212020
Cost of hosting and professional services$7,206 $6,563 
Cost of product and licensing29 75 
Cost of maintenance and support471 426 
Research and development9,364 8,440 
Sales and marketing11,710 8,943 
General and administrative9,619 10,459 
Total$38,399 $34,906 
Summary of Stock Options Activity
The table below summarizes activities related to stock options for the three months ended December 31, 2021:
Number of
Shares		Weighted
Average
Exercise
Price		Weighted
Average
Remaining
Contractual
Term
Aggregate
Intrinsic
Value (a)
Outstanding at September 30, 20219,355 $17.18 
Exercised(3,700)$17.18 
Outstanding at December 31, 20215,655 $17.18 0.3 years$0.2  million
Exercisable at December 31, 20215,655 $17.18 0.3 years$0.2  million
Exercisable at December 31, 20209,355 $17.18 1.3 years$0.3  million
__________
(a)The aggregate intrinsic value in this table represents any excess of the closing market price of our common stock as of December 31, 2021 ($55.32) over the exercise price of the underlying options.
Summary of Activity Relating to Restricted Units and Restricted Stock Awards The table below summarizes activities relating to restricted units and performance stock units for the three months ended December 31, 2021:
Number of Shares Underlying Restricted Units — Performance-Based AwardsNumber of Shares Underlying Restricted Units — Time-Based Awards
Outstanding at September 30, 20212,463,921 4,655,825 
Granted (a)
880,362 1,796,045 
Earned/released(1,760,724)(2,110,257)
Forfeited(5,601)(34,455)
Outstanding at December 31, 20211,577,958 4,307,158 
Weighted average remaining recognition period of outstanding Restricted Units1.2 years1.8 years
Unrecognized stock-based compensation expense of outstanding Restricted Units$21.1 million$122.3 million
Aggregate intrinsic value of outstanding Restricted Units (b)
$87.3 million$238.3 million
__________
(a)For the three months ending December 31, 2021, there were no performance-based restricted units granted. The granted performance-based restricted units for the period are a result of the performance-based restricted units vesting above their specified targets in our first quarter of fiscal year 2022.
(b)The aggregate intrinsic value in this table represents any excess of the closing market price of our common stock as of December 31, 2021 ($55.32) over the purchase price of the underlying restricted units.
Summary of Weighted-Average Grant-Date Fair Value and Intrinsic Value of Restricted Units and Restricted Stock Awards Vested
A summary of the weighted-average grant-date fair value of restricted units granted, and the aggregate intrinsic value of restricted units vested during the periods noted is as follows: 
 Three Months Ended December 31,
20212020
Weighted-average grant-date fair value per share$55.18 $37.26 
Total intrinsic value of shares vested (in millions)$213.4 $119.4 
Schedule of Key Assumptions of the Valuation Below is a summary of key assumptions of the valuation:
Three Months Ended December 31,
20212020
Dividend yield
N/A
0.0%
Expected volatility
N/A
34.95%
Risk-free interest rate
N/A
 0.21%
Expected term (in years)
N/A
3.00