Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7671)

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/07.22.03.7671.01

Input Form

HypergeometricPFQ[{6}, {-(23/4), 7/4}, -z] == (1/(3876364800 z^(3/4))) (4 z^(3/4) (521118675 - 741460500 z - 105809760 z^2 + 8808896 z^3 + 1153024 z^4 - 16384 z^5) - Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((-1343917575 - 1654052400 z + 5814244800 z^2 + 700976640 z^3 - 81600000 z^4 - 9846784 z^5 + 131072 z^6) Cos[2 Sqrt[z]] + 2 Sqrt[z] (-1343917575 - 3445942500 z + 741817440 z^2 + 282809280 z^3 + 19671040 z^4 + 1294336 z^5) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (-2 Sqrt[z] (-1343917575 - 3445942500 z + 741817440 z^2 + 282809280 z^3 + 19671040 z^4 + 1294336 z^5) Cos[2 Sqrt[z]] + (-1343917575 - 1654052400 z + 5814244800 z^2 + 700976640 z^3 - 81600000 z^4 - 9846784 z^5 + 131072 z^6) 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]