Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6787)

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=-23/4

http://functions.wolfram.com/07.22.03.6787.01

Input Form

HypergeometricPFQ[{3}, {-(23/4), -(21/4)}, -z] == (1/316234143225) (316234143225 - 31426995600 z + 3113510400 z^2 - 425779200 z^3 + 103219200 z^4 - 66060288 z^5 + 469762048 z^6 - 8388608 z^7 - 1048576 Sqrt[Pi] z^(25/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((-957 + 16 z) Cos[2 Sqrt[z]] + 256 Sqrt[z] Sin[2 Sqrt[z]]) + 1048576 Sqrt[Pi] z^(25/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] (-256 Sqrt[z] Cos[2 Sqrt[z]] + (-957 + 16 z) 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]