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

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, a₂>=5

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

For fixed z and a₁=5, a₂=11/2, b₁=-3/2

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

Input Form

HypergeometricPFQ[{5, 11/2}, {-(3/2), -(1/2)}, -z] == (1/8505) (8505 - 311850 z - 24324300 z^2 + 385945560 z^3 - 1076755680 z^4 + 1118269152 z^5 - 557051040 z^6 + 150109800 z^7 - 23204808 z^8 + 2095404 z^9 - 108136 z^10 + 2928 z^11 - 32 z^12) + (1/8505) ((2 Sqrt[Pi] (45405360 z^(5/2) - 343783440 z^(7/2) + 736215480 z^(9/2) - 671547240 z^(11/2) + 311341590 z^(13/2) - 80393418 z^(15/2) + 12100977 z^(17/2) - 1074024 z^(19/2) + 54792 z^(21/2) - 1472 z^(23/2) + 16 z^(25/2)) 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]