Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7751)

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=6, b₁>=-23/4

For fixed z and a₁=6, b₁=-15/4

http://functions.wolfram.com/07.22.03.7751.01

Input Form

HypergeometricPFQ[{6}, {-(15/4), -(1/4)}, -z] == (1/1663200) (4 (415800 - 2661120 z + 705285 z^2 + 1305540 z^3 - 328320 z^4 + 1024 z^5) + Sqrt[Pi] z^(5/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((-15663375 + 11138400 z + 12852000 z^2 - 2688000 z^3 + 8192 z^4) Cos[2 Sqrt[z]] + 6 Sqrt[z] (-5221125 - 3248700 z - 1904000 z^2 + 41984 z^3) Sin[2 Sqrt[z]]) - Sqrt[Pi] z^(5/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] (-6 Sqrt[z] (-5221125 - 3248700 z - 1904000 z^2 + 41984 z^3) Cos[2 Sqrt[z]] + (-15663375 + 11138400 z + 12852000 z^2 - 2688000 z^3 + 8192 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]