Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.am14)

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=9/2, b₁>=-11/2

For fixed z and a₁=4, a₂=9/2, b₁=-5/2

http://functions.wolfram.com/07.25.03.am14.01

Input Form

HypergeometricPFQ[{4, 9/2}, {-(5/2), -(5/2)}, z] == (1/70875) (70875 + 204120 z + 1247400 z^2 + 64864800 z^3 + 2575132560 z^4 + 9790260480 z^5 + 12043729152 z^6 + 6698557440 z^7 + 1953292800 z^8 + 320625408 z^9 + 30363264 z^10 + 1629056 z^11 + 45568 z^12 + 512 z^13) + (1/70875) (64 E^z Sqrt[Pi] (6486480 z^(7/2) + 79999920 z^(9/2) + 217493640 z^(11/2) + 229801320 z^(13/2) + 117910170 z^(15/2) + 32816574 z^(17/2) + 5235111 z^(19/2) + 486807 z^(21/2) + 25806 z^(23/2) + 716 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]