Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8613)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.8613.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(9/2), 19/4}, -z] == -((11 (Sqrt[Pi] (241052750180116875 + 95624231476410000 z + 30147540958080000 z^2 + 15006775943577600 z^3 - 17150601078374400 z^4 + 3228348438282240 z^5 - 294322364743680 z^6 + 17249662402560 z^7 - 811748818944 z^8 + 68719476736 z^9) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (80350916726705625 - 4857103821024000 z + 1414329081984000 z^2 - 1124276697169920 z^3 + 205924657397760 z^4 - 18629001216000 z^5 + 1089378189312 z^6 - 51539607552 z^7 + 4294967296 z^8) Cos[2 Sqrt[z]] + (-241052750180116875 + 161498702049048000 z + 6550576800768000 z^2 - 1447540048281600 z^3 + 226929103994880 z^4 - 19734850437120 z^5 + 1141521776640 z^6 - 54760833024 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]])))/ (299243084615516160 z^(15/4)))

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]