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Fungrim entry: 73cf98

f(α) is holomorphic on αC(,0]   for all f{αRC ⁣(α,y),αRC ⁣(x,α)}f(\alpha) \text{ is holomorphic on } \alpha \in \mathbb{C} \setminus \left(-\infty, 0\right] \;\text{ for all } f \in \left\{\alpha \mapsto R_C\!\left(\alpha, y\right), \alpha \mapsto R_C\!\left(x, \alpha\right)\right\}
Assumptions:xC  and  yC{0}x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \setminus \left\{0\right\}
TeX:
f(\alpha) \text{ is holomorphic on } \alpha \in \mathbb{C} \setminus \left(-\infty, 0\right] \;\text{ for all } f \in \left\{\alpha \mapsto R_C\!\left(\alpha, y\right), \alpha \mapsto R_C\!\left(x, \alpha\right)\right\}

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
IsHolomorphicf(z) is holomorphic at z=cf(z) \text{ is holomorphic at } z = c Holomorphic predicate
CCC\mathbb{C} Complex numbers
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Infinity\infty Positive infinity
CarlsonRCRC ⁣(x,y)R_C\!\left(x, y\right) Degenerate Carlson symmetric elliptic integral of the first kind
Source code for this entry:
Entry(ID("73cf98"),
    Formula(All(IsHolomorphic(f(alpha), ForElement(alpha, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0)))), ForElement(f, Set(Fun(alpha, CarlsonRC(alpha, y)), Fun(alpha, CarlsonRC(x, alpha)))))),
    Variables(x, y),
    Assumptions(And(Element(x, CC), Element(y, SetMinus(CC, Set(0))))))

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2020-04-08 16:14:44.404316 UTC