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Business Combinations (Narrative) (Details)
$ in Thousands
3 Months Ended 9 Months Ended 12 Months Ended
Aug. 01, 2018
USD ($)
Jul. 01, 2018
USD ($)
Apr. 01, 2018
USD ($)
Feb. 01, 2018
USD ($)
Nov. 01, 2017
USD ($)
Oct. 01, 2017
USD ($)
Sep. 01, 2017
USD ($)
Jun. 01, 2017
USD ($)
Apr. 01, 2017
USD ($)
Jul. 02, 2016
USD ($)
Sep. 02, 2015
USD ($)
Sep. 30, 2018
USD ($)
Sep. 30, 2017
USD ($)
Sep. 30, 2018
USD ($)
Companies
Sep. 30, 2017
USD ($)
Dec. 31, 2017
USD ($)
Companies
Dec. 31, 2016
USD ($)
Jul. 01, 2016
Sep. 01, 2015
Business Acquisition [Line Items]                                      
Recognized controlling ownership of joint venture                           $ 2,292          
Non-operating income, gain on joint venture investment (see Note 8)                       $ 7 $ 0 $ 60 $ 0 $ 1,162      
Number of Businesses Acquired | Companies                           7   6      
Reduction of acquisition earnout accruals                           $ (645) (164)        
Goodwill, Translation and Purchase Accounting Adjustments [1]                           (13,718) (3,432) $ (4,007)      
Derivative Liability                       29,285   29,285   37,096 $ 8,510    
Business Combination, Contingent Consideration Arrangements, Change in Amount of Contingent Consideration, Liability                           14,363 $ 3,596        
Goodwill, Purchase Accounting Adjustments                           (12,745)   (12,158)      
Goodwill                       870,311   870,311   666,863 $ 441,404    
Fair Value of Joint Venture, excluding Noncontrolling Interest                 $ 120,000                    
Fair Value of Joint Venture, including Noncontrolling Interest                 150,000                    
Miles [Member]                                      
Business Acquisition [Line Items]                                      
Payments to Acquire Businesses, Gross $ 18,300                                    
Leisure [Member]                                      
Business Acquisition [Line Items]                                      
Payments to Acquire Businesses, Gross   $ 2,100                                  
Mercury [Member]                                      
Business Acquisition [Line Items]                                      
Payments to Acquire Businesses, Gross   13,200                                  
Indus [Member]                                      
Business Acquisition [Line Items]                                      
Payments to Acquire Businesses, Gross   22,900                                  
CDL (Centrum) [Member]                                      
Business Acquisition [Line Items]                                      
Payments to Acquire Businesses, Gross     $ 179,500                                
Transcorp [Member]                                      
Business Acquisition [Line Items]                                      
Payments to Acquire Businesses, Gross       $ 7,300                              
Payments to Acquire Businesses, Net       6,550                              
Business Combination, Consideration Transferred, Liabilities Incurred       $ 700                              
Via [Member]                                      
Business Acquisition [Line Items]                                      
Payments to Acquire Businesses, Gross         $ 78,800                            
Derivative, Term of Contract         12 months                            
PML [Member]                                      
Business Acquisition [Line Items]                                      
Payments to Acquire Businesses, Gross         $ 37,400                            
Wallstreet [Member]                                      
Business Acquisition [Line Items]                                      
Payments to Acquire Businesses, Gross           $ 7,400                          
YouFirst [Member]                                      
Business Acquisition [Line Items]                                      
Payments to Acquire Businesses, Gross             $ 10,200                        
beBetter [Member]                                      
Business Acquisition [Line Items]                                      
Payments to Acquire Businesses, Gross               $ 1,000                      
Derivative Liability                       0   0          
Derivative, Term of Contract               24 months                      
ItzCash [Member]                                      
Business Acquisition [Line Items]                                      
Payments to Acquire Businesses, Gross                 $ 76,300                    
Derivative Liability                       14,790   14,790          
Derivative, Term of Contract                 36 months                    
Payments to Acquire Business, Held in Escrow                 $ 3,800                    
Escrow Derivative, Term of Contract                 12 months                    
Maximum [Member] | Miles [Member]                                      
Business Acquisition [Line Items]                                      
Derivative Liability $ 8,300                                    
Maximum [Member] | Indus [Member]                                      
Business Acquisition [Line Items]                                      
Derivative Liability   $ 5,000                                  
Maximum [Member] | beBetter [Member]                                      
Business Acquisition [Line Items]                                      
Derivative Liability               $ 2,000                      
Maximum [Member] | ItzCash [Member]                                      
Business Acquisition [Line Items]                                      
Derivative Liability                 $ 44,000                    
Potential claims made by tax authorities [Member] | Via [Member]                                      
Business Acquisition [Line Items]                                      
Derivative Liability         2,300                            
Refund of Advance and withholding taxes [Member] | Via [Member]                                      
Business Acquisition [Line Items]                                      
Derivative Liability         $ 2,000                            
Contingent accrued earn-out acquisition consideration [Member]                                      
Business Acquisition [Line Items]                                      
Derivative Liability                       29,285   29,285   37,096      
Contingent liability for accrued earn-out acquisition consideration                       15,100   15,100   33,100      
Business acquisition, contingent consideration, at fair value, current                       $ 14,200   $ 14,200   $ 4,000      
Smartclass [Member]                                      
Business Acquisition [Line Items]                                      
Payments to Acquire Interest in Joint Venture     $ 8,600                                
Equity Method Investment, Ownership Percentage     60.00%                                
ItzCash [Member]                                      
Business Acquisition [Line Items]                                      
Equity Method Investment, Ownership Percentage                 80.00%                    
EbixHealth JV [Member]                                      
Business Acquisition [Line Items]                                      
Equity Method Investment, Ownership Percentage Increase (Decrease)                   11.00%                  
Payments to Acquire Interest in Joint Venture                   $ 2,000 $ 6,000                
Equity Method Investment, Ownership Percentage                                   51.00% 40.00%
[1] Recorded as an adjustment to reported general and administrative expenses