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

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.ambk.01

Input Form

HypergeometricPFQ[{4, 11/2}, {-(7/2), 1/2}, z] == (1/297675) (297675 - 3742200 z + 16216200 z^2 - 64864800 z^3 + 551350800 z^4 + 1649007360 z^5 + 1386927360 z^6 + 524482560 z^7 + 103668480 z^8 + 11325120 z^9 + 681792 z^10 + 20992 z^11 + 256 z^12) + (1/297675) (32 E^z Sqrt[Pi] (32432400 z^(9/2) + 67813200 z^(11/2) + 50274000 z^(13/2) + 17856720 z^(15/2) + 3406725 z^(17/2) + 364245 z^(19/2) + 21630 z^(21/2) + 660 z^(23/2) + 8 z^(25/2)) 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]