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

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=3, a₂>=3

For fixed z and a₁=3, a₂=9/2, b₁>=-11/2

For fixed z and a₁=3, a₂=9/2, b₁=-5/2

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

Input Form

HypergeometricPFQ[{3, 9/2}, {-(5/2), -(5/2)}, z] == (1/23625) (23625 + 51030 z + 249480 z^2 + 10810800 z^3 + 358752240 z^4 + 1139513760 z^5 + 1165049088 z^6 + 531445248 z^7 + 124220160 z^8 + 15752192 z^9 + 1083648 z^10 + 37632 z^11 + 512 z^12) + (1/23625) (128 E^z Sqrt[Pi] (498960 z^(7/2) + 5266800 z^(9/2) + 12174120 z^(11/2) + 10813320 z^(13/2) + 4584930 z^(15/2) + 1028118 z^(17/2) + 127155 z^(19/2) + 8611 z^(21/2) + 296 z^(23/2) + 4 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]