Assumptions:
TeX:
R_{-a}\!\left(\left[b_{1}, b_{2}, \ldots, b_{n}\right], \left[\lambda z_{1}, \lambda z_{2}, \ldots, \lambda z_{n}\right]\right) = {\lambda}^{-a} R_{-a}\!\left(\left[b_{1}, b_{2}, \ldots, b_{n}\right], \left[z_{1}, z_{2}, \ldots, z_{n}\right]\right)
a \in \mathbb{R} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \left(b_{k} \in \mathbb{R} \;\text{ for all } k \in \{1, 2, \ldots, n\}\right) \;\mathbin{\operatorname{and}}\; \left(z_{k} \in \mathbb{C} \setminus \left(-\infty, 0\right] \;\text{ for all } k \in \{1, 2, \ldots, n\}\right) \;\mathbin{\operatorname{and}}\; \sum_{k=1}^{n} b_{k} > a > 0 \;\mathbin{\operatorname{and}}\; \lambda \in \left(0, \infty\right)Definitions:
| Fungrim symbol | Notation | Short description |
|---|---|---|
| CarlsonHypergeometricR | Carlson multivariate hypergeometric function | |
| Pow | Power | |
| RR | Real numbers | |
| ZZGreaterEqual | Integers greater than or equal to n | |
| Range | Integers between given endpoints | |
| CC | Complex numbers | |
| OpenClosedInterval | Open-closed interval | |
| Infinity | Positive infinity | |
| Sum | Sum | |
| OpenInterval | Open interval |
Source code for this entry:
Entry(ID("2c1df7"),
Formula(Equal(CarlsonHypergeometricR(Neg(a), List(b_(k), For(k, 1, n)), List(Mul(lamda, z_(k)), For(k, 1, n))), Mul(Pow(lamda, Neg(a)), CarlsonHypergeometricR(Neg(a), List(b_(k), For(k, 1, n)), List(z_(k), For(k, 1, n)))))),
Variables(a, b_, z_, n, lamda),
Assumptions(And(Element(a, RR), Element(n, ZZGreaterEqual(1)), All(Element(b_(k), RR), ForElement(k, Range(1, n))), All(Element(z_(k), SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0))), ForElement(k, Range(1, n))), Greater(Sum(b_(k), For(k, 1, n)), a, 0), Element(lamda, OpenInterval(0, Infinity)))))