Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7663)

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=-23/4

http://functions.wolfram.com/07.22.03.7663.01

Input Form

HypergeometricPFQ[{6}, {-(23/4), -(9/4)}, -z] == (1/1022088375) (1022088375 - 474012000 z + 279417600 z^2 - 794787840 z^3 + 499554720 z^4 + 233055360 z^5 - 19271680 z^6 + 32768 z^7 + 8 Sqrt[Pi] z^(13/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((-128118375 + 144698400 z + 65076000 z^2 - 4899840 z^3 + 8192 z^4) Cos[2 Sqrt[z]] + 2 Sqrt[z] (-128118375 - 26126100 z - 15312000 z^2 + 166912 z^3) Sin[2 Sqrt[z]]) - 8 Sqrt[Pi] z^(13/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] (-2 Sqrt[z] (-128118375 - 26126100 z - 15312000 z^2 + 166912 z^3) Cos[2 Sqrt[z]] + (-128118375 + 144698400 z + 65076000 z^2 - 4899840 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]