Returns one of the following transforms 1. ₂F₁(a,b;c;x) = (1-x)^{-b} ₂F₁(b,c-a;c;x/(x-1)) 2. ₂F₁(a,b;c;x) = (1-x)^{-a} ₂F₁(a,c-b;c;x/(x-1)) 3. ₂F₁(a,b;c;x) = (1-x)^{-a} Γ(c)Γ(b-a)/(Γ(b)Γ(c-a)) ₂F₁(a,c-b;a-b+1;1/(1-x)) + (1-x)^{-b} Γ(c)Γ(a-b)/(Γ(a)Γ(c-b)) ₂F₁(b,c-a;b-a+1;1/(1-x)) 4. ₂F₁(a,b;c;x) = Γ(c)Γ(c-a-b)/Γ(c-a)Γ(c-b) ₂F₁(c-a, c-b, c-a-b+1, 1-x) + (1-x)^(c-a-b) Γ(c)Γ(a+b-c)/Γ(a)Γ(b) ₂F₁(c-a,c-b;c-a-b+1;1-x) Regions of validity: 1. |a| < |b|, -1 ≤ x < 0 2. |a| > |b|, -1 ≤ x < 0 3. -∞ < x < -1 4. ½ < x < 1
Assumes that x is on the real axis
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in) | :: | a | |||
| complex(kind=dp), | intent(in) | :: | b | |||
| complex(kind=dp), | intent(in) | :: | c | |||
| real(kind=dp), | intent(in) | :: | x |