Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.amc6)

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.amc6.01

Input Form

HypergeometricPFQ[{4, 11/2}, {-(5/2), -(1/2)}, z] == (1/42525) (42525 + 748440 z - 16216200 z^2 + 324324000 z^3 + 2198916720 z^4 + 3424861440 z^5 + 2205874944 z^6 + 715668480 z^7 + 127783680 z^8 + 12973056 z^9 + 738624 z^10 + 21760 z^11 + 256 z^12) + (1/42525) (32 E^z Sqrt[Pi] (25945920 z^(7/2) + 103783680 z^(9/2) + 133857360 z^(11/2) + 78533280 z^(13/2) + 24184440 z^(15/2) + 4185216 z^(17/2) + 416619 z^(19/2) + 23418 z^(21/2) + 684 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]