The *hypergeometric function*,

where is a *Pochhammer symbol* is, for rational {*a, b, c, z*}, generally not a rational value. In the link given above, equations (18) and (19) are,

There are in fact an infinite number of such equalities. One given by M. Glasser is, let , then,

Another, based on eq. (42) of Vidunas’ “*Transformations of algebraic Gauss hypergeometric functions*” is, let , then,

A third which yields not a rational but an algebraic number is remarkable for its connection to the *Rogers-Ramanujan continued fraction*. Let where,

then,

If the polynomials are familiar, it is because they are invariants of the *icosahedron*. They also appear in the *j-function* formula,

where,

and

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