Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9861)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=-5/2

http://functions.wolfram.com/07.22.03.9861.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(5/2), 19/4}, -z] == -((11 (Sqrt[Pi] (35983393070625 + 16748633865600 z + 6380431948800 z^2 + 4003408281600 z^3 - 6159089664000 z^4 + 1751918837760 z^5 - 311452237824 z^6 + 109521666048 z^7 + 4294967296 z^8) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (11994464356875 + 99694249200 z + 460808974080 z^2 - 422526504960 z^3 + 115271073792 z^4 - 20639121408 z^5 + 6794772480 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + (-35983393070625 + 21633652076400 z + 1736895363840 z^2 - 644138127360 z^3 + 144155934720 z^4 - 24892145664 z^5 + 6593445888 z^6 + 268435456 z^7) Sin[2 Sqrt[z]])))/ (98956046499840 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]