Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ambe)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=4, a₂>=4

For fixed z and a₁=4, a₂=11/2, b₁>=-11/2

For fixed z and a₁=4, a₂=11/2, b₁=-7/2

http://functions.wolfram.com/07.25.03.ambe.01

Input Form

HypergeometricPFQ[{4, 11/2}, {-(7/2), -(5/2)}, z] == (1/4465125) (4465125 + 11226600 z + 48648600 z^2 + 972972000 z^3 - 57891834000 z^4 - 774745171200 z^5 - 1981051188480 z^6 - 1987168619520 z^7 - 996372576000 z^8 - 280830044160 z^9 - 47321856000 z^10 - 4901707776 z^11 - 312041472 z^12 - 11804160 z^13 - 241664 z^14 - 2048 z^15) - (1/4465125) (256 E^z Sqrt[Pi] (778377600 z^(9/2) + 5236358400 z^(11/2) + 10490860800 z^(13/2) + 9324201600 z^(15/2) + 4367351520 z^(17/2) + 1181174400 z^(19/2) + 193868640 z^(21/2) + 19734840 z^(23/2) + 1241505 z^(25/2) + 46578 z^(27/2) + 948 z^(29/2) + 8 z^(31/2)) Erf[Sqrt[z]])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]