ELLIPTIC HYPERGEOMETRIC FUNCTION AND 6 j -SYMBOLS FOR THE SL (2 , C ) GROUP

We show that the complex hypergeometric function describing 6 j -symbols for the SL (2 , C ) group is a special degeneration of the V -function—an elliptic analogue of the Euler–Gauss 2 F 1 hypergeometric function. For this function, we derive mixed difference–recurrence relations as limit forms of the elliptic hypergeometric equation and some symmetry transformations. At the intermediate steps of computations, there emerge a function describing the 6 j -symbols for the Faddeev modular double and the corresponding difference equations and symmetry transformations.

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