Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7723)

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/07.22.03.7723.01

Input Form

HypergeometricPFQ[{6}, {-(19/4), 23/4}, -z] == (1/(62914560 z^(19/4))) (4 z^(3/4) (-756212081625 + 242594352000 z - 36356720400 z^2 + 3355672320 z^3 - 235418880 z^4 + 5038080 z^5 + 851968 z^6) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (5 (453727248975 - 923374752300 z + 335091556800 z^2 - 52540488000 z^3 + 4947022080 z^4 - 356428800 z^5 + 8945664 z^6 + 1310720 z^7) Cos[2 Sqrt[z]] + 2 Sqrt[z] (2268636244875 - 1592025435000 z + 359383424400 z^2 - 42291849600 z^3 + 3401798400 z^4 - 198481920 z^5 - 5898240 z^6 + 524288 z^7) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (2268636244875 - 1592025435000 z + 359383424400 z^2 - 42291849600 z^3 + 3401798400 z^4 - 198481920 z^5 - 5898240 z^6 + 524288 z^7) Cos[2 Sqrt[z]] - 5 (453727248975 - 923374752300 z + 335091556800 z^2 - 52540488000 z^3 + 4947022080 z^4 - 356428800 z^5 + 8945664 z^6 + 1310720 z^7) 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]