Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8vb)

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

For fixed z and a₁=-11/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.a8vb.01

Input Form

HypergeometricPFQ[{-(11/4)}, {-(9/2), 21/4}, -z] == (221 (Sqrt[Pi] (285447819281625 + 70264078592400 z + 12088443628800 z^2 + 2387840716800 z^3 + 1661106585600 z^4 - 279765319680 z^5 + 14210301952 z^6 - 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-285447819281625 + 234213595308000 z - 14467756343040 z^2 + 124043673600 z^3 - 18379898880 z^4 + 903872512 z^5 - 16777216 z^6) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-95149273093875 + 20075451026400 z - 352361560320 z^2 - 107504517120 z^3 + 17658740736 z^4 - 891289600 z^5 + 16777216 z^6) Sin[2 Sqrt[z]])))/ (346346162749440 z^(17/4))

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]