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

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=6, b₁>=-11/2

For fixed z and a₁=7/2, a₂=6, b₁=-5/2

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

Input Form

HypergeometricPFQ[{7/2, 6}, {-(5/2), -(5/2)}, -z] == (1/50625) (50625 - 170100 z + 1190700 z^2 - 69854400 z^3 + 3141309600 z^4 - 13590720000 z^5 + 19157093280 z^6 - 12352901760 z^7 + 4250774520 z^8 - 845111760 z^9 + 100809900 z^10 - 7257888 z^11 + 306176 z^12 - 6912 z^13 + 64 z^14) - (1/50625) ((2 Sqrt[Pi] (-236293200 z^(7/2) + 3255595200 z^(9/2) - 9958923000 z^(11/2) + 11962458000 z^(13/2) - 7077053250 z^(15/2) + 2315363040 z^(17/2) - 446119965 z^(19/2) + 52147050 z^(21/2) - 3703800 z^(23/2) + 154800 z^(25/2) - 3472 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]