Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.amc4)

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=-5/2

http://functions.wolfram.com/07.25.03.amc4.01

Input Form

HypergeometricPFQ[{4, 11/2}, {-(5/2), -(3/2)}, z] == (1/127575) (127575 + 748440 z + 16216200 z^2 - 972972000 z^3 - 12655122480 z^4 - 30616185600 z^5 - 28419745536 z^6 - 12898483200 z^7 - 3208992000 z^8 - 462449664 z^9 - 39220224 z^10 - 1912192 z^11 - 49152 z^12 - 512 z^13) - (1/127575) (64 E^z Sqrt[Pi] (51891840 z^(7/2) + 337296960 z^(9/2) + 639213120 z^(11/2) + 526523760 z^(13/2) + 223639920 z^(15/2) + 53480952 z^(17/2) + 7518168 z^(19/2) + 627381 z^(21/2) + 30258 z^(23/2) + 772 z^(25/2) + 8 z^(27/2)) 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]