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

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=11/2, a₂>=11/2

For fixed z and a₁=11/2, a₂=6, b₁>=-11/2

For fixed z and a₁=11/2, a₂=6, b₁=-5/2

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

Input Form

HypergeometricPFQ[{11/2, 6}, {-(5/2), -(1/2)}, z] == (1/212625) (212625 + 5613300 z - 170270100 z^2 + 4540536000 z^3 + 43005362400 z^4 + 92626934400 z^5 + 83444437440 z^6 + 38823909120 z^7 + 10351980000 z^8 + 1671015360 z^9 + 167248620 z^10 + 10352544 z^11 + 382592 z^12 + 7680 z^13 + 64 z^14) + (1/212625) (2 E^z Sqrt[Pi] (6616209600 z^(7/2) + 35286451200 z^(9/2) + 61400430000 z^(11/2) + 49590727200 z^(13/2) + 21666544200 z^(15/2) + 5557597920 z^(17/2) + 874953765 z^(19/2) + 86121450 z^(21/2) + 5270040 z^(23/2) + 193200 z^(25/2) + 3856 z^(27/2) + 32 z^(29/2)) 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]