Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aj4d)

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=4, b₁>=-11/2

For fixed z and a₁=5/2, a₂=4, b₁=-11/2

http://functions.wolfram.com/07.25.03.aj4d.01

Input Form

HypergeometricPFQ[{5/2, 4}, {-(11/2), -(11/2)}, z] == (1/972504225) (972504225 + 321489000 z + 138915000 z^2 + 102060000 z^3 + 157172400 z^4 + 726485760 z^5 + 32691859200 z^6 + 1187812684800 z^7 + 4310966580480 z^8 + 5239582709760 z^9 + 2969681504256 z^10 + 911054807040 z^11 + 163268259840 z^12 + 17711038464 z^13 + 1168113664 z^14 + 45422592 z^15 + 950272 z^16 + 8192 z^17) + (1/972504225) (1024 E^z Sqrt[Pi] (195350400 z^(13/2) + 2266064640 z^(15/2) + 5961634560 z^(17/2) + 6261534720 z^(19/2) + 3282420960 z^(21/2) + 962015040 z^(23/2) + 167570592 z^(25/2) + 17845248 z^(27/2) + 1162461 z^(29/2) + 44818 z^(31/2) + 932 z^(33/2) + 8 z^(35/2)) 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]