Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7685)

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=6, b₁>=-23/4

For fixed z and a₁=6, b₁=-21/4

http://functions.wolfram.com/07.22.03.7685.01

Input Form

HypergeometricPFQ[{6}, {-(21/4), -(11/4)}, -z] == (1/723647925) (723647925 - 300736800 z + 141523200 z^2 - 154828800 z^3 + 609668640 z^4 + 397450368 z^5 - 21188608 z^6 + 32768 z^7 - 16 Sqrt[Pi] z^(15/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] ((38405745 - 24256260 z + 18748800 z^2 - 173056 z^3) Cos[2 Sqrt[z]] + 2 Sqrt[z] (38405745 + 26951400 z - 1345536 z^2 + 2048 z^3) Sin[2 Sqrt[z]]) + 16 Sqrt[Pi] z^(15/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (38405745 + 26951400 z - 1345536 z^2 + 2048 z^3) Cos[2 Sqrt[z]] + (-38405745 + 24256260 z - 18748800 z^2 + 173056 z^3) 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]