Geodesic
Elliptic hypergeometric function and $6j$-symbols for the~$SL(2,\pmb{\mathbb C})$ group
Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 1, pp. 108-128

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We show that the complex hypergeometric function describing $6j$-symbols for the $SL(2,\mathbb C)$ group is a special degeneration of the $V$-function—an elliptic analogue of the Euler–Gauss ${}_2F_1$ 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 $6j$-symbols for the Faddeev modular double and the corresponding difference equations and symmetry transformations.
Keywords: $6j$-symbols, $SL(2,\mathbb{C})$ group, elliptic hypergeometric function. 
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     title = {Elliptic hypergeometric function and $6j$-symbols for the~$SL(2,\pmb{\mathbb C})$ group},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2022_213_1_a6/}
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S. E. Derkachov; G. A. Sarkissian; V. P. Spiridonov. Elliptic hypergeometric function and $6j$-symbols for the~$SL(2,\pmb{\mathbb C})$ group. Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 1, pp. 108-128. http://geodesic.mathdoc.fr/item/TMF_2022_213_1_a6/