Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8kp)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.a8kp.01

Input Form

HypergeometricPFQ[{-(13/4)}, {-(1/2), 23/4}, -z] == -((209 (Sqrt[Pi] (8890014758625 + 3612450441600 z + 1081803340800 z^2 + 380414361600 z^3 + 281788416000 z^4 - 721378344960 z^5 + 1154205351936 z^6 + 195421011968 z^7 + 4294967296 z^8) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (2963338252875 - 150518768400 z + 29068865280 z^2 + 32959180800 z^3 - 54283665408 z^4 + 69957844992 z^5 + 12163481600 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + (-8890014758625 + 5870231967600 z + 363176835840 z^2 + 64358461440 z^3 - 76485427200 z^4 + 61678288896 z^5 + 11962155008 z^6 + 268435456 z^7) Sin[2 Sqrt[z]])))/ (184717953466368 z^(19/4)))

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]