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

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=6, b₁>=-11/2

For fixed z and a₁=5/2, a₂=6, b₁=-11/2

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

Input Form

HypergeometricPFQ[{5/2, 6}, {-(11/2), -(1/2)}, -z] == (1/467775) (467775 - 2551500 z - 13891500 z^2 - 31752000 z^3 - 62868960 z^4 - 155675520 z^5 - 951350400 z^6 + 1895780160 z^7 - 1166986080 z^8 + 339130848 z^9 - 53247852 z^10 + 4736160 z^11 - 236672 z^12 + 6144 z^13 - 64 z^14) + (1/467775) ((2 Sqrt[Pi] (786285360 z^(13/2) - 1179428040 z^(15/2) + 657440280 z^(17/2) - 181827765 z^(19/2) + 27752490 z^(21/2) - 2425752 z^(23/2) + 119856 z^(25/2) - 3088 z^(27/2) + 32 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]