Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.alg5)

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=5, b₁>=-11/2

For fixed z and a₁=7/2, a₂=5, b₁=-3/2

http://functions.wolfram.com/07.25.03.alg5.01

Input Form

HypergeometricPFQ[{7/2, 5}, {-(3/2), -(3/2)}, -z] == (1/405) (405 - 3150 z + 170100 z^2 - 6569640 z^3 + 23371920 z^4 - 26131248 z^5 + 12838800 z^6 - 3198670 z^7 + 429042 z^8 - 31036 z^9 + 1128 z^10 - 16 z^11) + ((1/405) Sqrt[Pi] (-1081080 z^(5/2) + 12818520 z^(7/2) - 32586840 z^(9/2) + 31366920 z^(11/2) - 14257545 z^(13/2) + 3399009 z^(15/2) - 444016 z^(17/2) + 31592 z^(19/2) - 1136 z^(21/2) + 16 z^(23/2)) Erfi[Sqrt[z]])/E^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]