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

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=5/2, a₂>=5/2

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

For fixed z and a₁=5/2, a₂=5, b₁=-9/2

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

Input Form

HypergeometricPFQ[{5/2, 5}, {-(9/2), -(5/2)}, -z] == (1/127575) (127575 - 141750 z + 283500 z^2 - 2381400 z^3 - 34927200 z^4 - 544864320 z^5 + 2909088000 z^6 - 3769430400 z^7 + 2080946880 z^8 - 590483520 z^9 + 93588432 z^10 - 8531280 z^11 + 440160 z^12 - 11840 z^13 + 128 z^14) - (1/127575) ((8 Sqrt[Pi] (-158722200 z^(11/2) + 525004200 z^(13/2) - 575062740 z^(15/2) + 292283460 z^(17/2) - 79188795 z^(19/2) + 12206025 z^(21/2) - 1093200 z^(23/2) + 55752 z^(25/2) - 1488 z^(27/2) + 16 z^(29/2)) 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]