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Hypergeometric Functions
MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z]
Series representations
Main terms of asymptotic expansions
Expansions at z==(-1)m+n-q for p==q
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http://functions.wolfram.com/07.34.06.0041.01
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MeijerG[{{Subscript[a, 1], \[Ellipsis], Subscript[a, n]},
{Subscript[a, n + 1], \[Ellipsis], Subscript[a, q]}},
{{Subscript[b, 1], \[Ellipsis], Subscript[b, m]},
{Subscript[b, m + 1], \[Ellipsis], Subscript[b, q]}}, z] \[Proportional]
c (1 + O[z - (-1)^(m + n - q)]) +
d (1 - (-1)^(q - m - n) z)^Subscript[\[Psi], q]
(1 + O[z - (-1)^(m + n - q)]) /; (z -> (-1)^(m + n - q)) && Abs[z] < 1 &&
Subscript[\[Psi], q] == Sum[Subscript[a, j] - Subscript[b, j], {j, 1, q}] -
1 && c == MeijerG[{{Subscript[a, 1], \[Ellipsis], Subscript[a, n]},
{Subscript[a, n + 1], \[Ellipsis], Subscript[a, q]}},
{{Subscript[b, 1], \[Ellipsis], Subscript[b, m]},
{Subscript[b, m + 1], \[Ellipsis], Subscript[b, q]}},
(-1)^(m + n - q)] && d == Pi^(m + n - q - 1) Gamma[-Subscript[\[Psi], q]]
Sum[(Product[Sin[(Subscript[a, k] - Subscript[b, h]) Pi], {k, n + 1, q}]/
Product[If[k == h, 1, Sin[(Subscript[b, k] - Subscript[b, h]) Pi]],
{k, 1, m}]) E^((m + n - q) Pi I Subscript[b, h]), {h, 1, m}] &&
!Element[Subscript[\[Psi], q], Integers]
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Date Added to functions.wolfram.com (modification date)
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| MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z,r] | | |
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){kind=small}
