Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7129)

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=4, b₁>=-23/4

For fixed z and a₁=4, b₁=-19/4

http://functions.wolfram.com/07.22.03.7129.01

Input Form

HypergeometricPFQ[{4}, {-(19/4), -(5/4)}, -z] == (1/987525) (987525 - 665280 z + 1774080 z^2 - 1249920 z^3 - 453120 z^4 + 8192 z^5 + 32 Sqrt[Pi] z^(9/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((69615 - 85680 z - 30240 z^2 + 512 z^3) Cos[2 Sqrt[z]] + 42 Sqrt[z] (3315 + 340 z + 192 z^2) Sin[2 Sqrt[z]]) - 32 Sqrt[Pi] z^(9/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] (-42 Sqrt[z] (3315 + 340 z + 192 z^2) Cos[2 Sqrt[z]] + (69615 - 85680 z - 30240 z^2 + 512 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]