Bone and BInf are not fully accurate in BigFloat

[MikaelSlevinsky]

julia> using HypergeometricFunctions

julia> a, b, c = (big(1)/2, big(1)/2, big"1.0")
(0.5, 0.5, 1.0)

julia> α = big"1e4"
10000.0

julia> z = 1-1/α^2
0.9999999900000000000000000000000000000000000000000000000000000000000000000000026

julia> F = _₂F₁(a, b, c, z)
6.746027206919546933185707950465181792044092589816046355200686957659126835747708

julia> W = HypergeometricFunctions.pFqweniger((a, b), (c, ), z)
6.746027206919546933185707368349657796992000329097040770443860355283388186516648

julia> G2 = HypergeometricFunctions._₂F₁general2(a, b, c, z)
6.746027206919546933185707368349657796992000329097040770443860355283388258457107

julia> F-W
5.821155239950520922607190055847568266023757386492310599016275842944951993501008e-25

julia> F-G2
5.821155239950520922607190055847568266023757385772906013187673677205578357891202e-25

julia> W-G2
-7.194045858286021657393736356098066928173795481180378727151581313017631264882825e-71

The issue is that the tolerance is fixed to Float64

[MikaelSlevinsky]

Now the three methods agree

julia> using HypergeometricFunctions
[ Info: Precompiling HypergeometricFunctions [34004b35-14d8-5ef3-9330-4cdb6864b03a]

julia> a, b, c = (big(1)/2, big(1)/2, big"1.0")
(0.5, 0.5, 1.0)

julia> α = big"1e4"
10000.0

julia> z = 1-1/α^2
0.9999999900000000000000000000000000000000000000000000000000000000000000000000026

julia> F = _₂F₁(a, b, c, z)
6.746027206919546933185707368349657796992000329097040770443860355283388258457591

julia> W = HypergeometricFunctions.pFqweniger((a, b), (c, ), z)
6.746027206919546933185707368349657796992000329097040770443860355283388186516648

julia> G2 = HypergeometricFunctions._₂F₁general2(a, b, c, z)
6.746027206919546933185707368349657796992000329097040770443860355283388258457107

julia> F-W
7.194094220829930186283638519668498610411393730782419570327337445757064208996922e-71

julia> F-G2
4.836254390852888990216357043168223759824960204084317575613273943294411409770959e-76

julia> W-G2
-7.194045858286021657393736356098066928173795481180378727151581313017631264882825e-71