The court hearing will decide whether the pension scheme is a final salary scheme or a money purchase scheme.
If the judge rules the scheme is final salary the firm could be forced to make good the shortfall.
The shortfall has long been contested by the firm.
Last year Accountancy Age reported that members could see their benefits slashed by as much as 20% if the firm does not make up the shortfall.
In January last year the trustees of the pension fund were changed from Capita to Aon Trust Corporation.
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