Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7703)

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=-19/4

http://functions.wolfram.com/07.22.03.7703.01

Input Form

HypergeometricPFQ[{6}, {-(19/4), -(17/4)}, -z] == (1/9820936125) (9820936125 - 2918916000 z + 838252800 z^2 - 361267200 z^3 + 371589120 z^4 - 3963617280 z^5 + 837017600 z^6 - 6029312 z^7 + 256 Sqrt[Pi] z^(21/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] (-5 (7258845 - 1347360 z + 9472 z^2) Cos[2 Sqrt[z]] + 4 Sqrt[z] (6416745 - 206240 z + 256 z^2) Sin[2 Sqrt[z]]) + 256 Sqrt[Pi] z^(21/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] (4 Sqrt[z] (6416745 - 206240 z + 256 z^2) Cos[2 Sqrt[z]] + 5 (7258845 - 1347360 z + 9472 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]