Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6815)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=3, b₁>=-23/4

For fixed z and a₁=3, b₁=-21/4

http://functions.wolfram.com/07.22.03.6815.01

Input Form

HypergeometricPFQ[{3}, {-(21/4), -(11/4)}, -z] == (1/48243195) (9 (5360355 - 1113840 z + 299520 z^2 - 204800 z^3 + 647168 z^4 + 163840 z^5) - 4096 Sqrt[Pi] z^(15/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] ((1311 - 1380 z + 64 z^2) Cos[2 Sqrt[z]] + 46 Sqrt[z] (57 + 16 z) Sin[2 Sqrt[z]]) - 4096 Sqrt[Pi] z^(15/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] (-46 Sqrt[z] (57 + 16 z) Cos[2 Sqrt[z]] + (1311 - 1380 z + 64 z^2) Sin[2 Sqrt[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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]