Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8657)

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`=-7/2

http://functions.wolfram.com/07.22.03.8657.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(7/2), 15/4}, -z] == (11 (Sqrt[Pi] (-68695568589375 - 50245901596800 z - 44663023641600 z^2 + 84071573913600 z^3 - 25868176588800 z^4 + 4087810621440 z^5 - 503115153408 z^6 + 135291469824 z^7 + 4294967296 z^8) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-22898522863125 - 6280737699600 z + 5836132028160 z^2 - 1690718883840 z^3 + 264170962944 z^4 - 32920043520 z^5 + 8405385216 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + (68695568589375 - 23029371565200 z + 9676988455680 z^2 - 2110181068800 z^3 + 307324846080 z^4 - 38381027328 z^5 + 8204058624 z^6 + 268435456 z^7) Sin[2 Sqrt[z]])))/ (1298798110310400 z^(11/4))

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]