Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7567)

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=5, b₁>=-23/4

For fixed z and a₁=5, b₁=-3/4

http://functions.wolfram.com/07.22.03.7567.01

Input Form

HypergeometricPFQ[{5}, {-(3/4), 19/4}, -z] == (1/(2097152 z^(15/4))) (385 (-4 z^(3/4) (-72765 + 28140 z - 6096 z^2 + 256 z^3) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (-218295 + 167580 z - 47856 z^2 + 10752 z^3 + 4096 z^4) Cos[2 Sqrt[z]] + (218295 - 458640 z + 193680 z^2 - 44544 z^3 + 4096 z^4) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((-218295 + 458640 z - 193680 z^2 + 44544 z^3 - 4096 z^4) Cos[2 Sqrt[z]] + 2 Sqrt[z] (-218295 + 167580 z - 47856 z^2 + 10752 z^3 + 4096 z^4) 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]