Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7rd)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.a7rd.01

Input Form

HypergeometricPFQ[{-(17/4)}, {3/2, 23/4}, -z] == (Sqrt[Pi] (1327152203251875 + 980050857786000 z + 633568231296000 z^2 + 675806113382400 z^3 + 5406448907059200 z^4 + 28834394170982400 z^5 + 8787624890204160 z^6 + 608666659061760 z^7 + 12485469929472 z^8 + 68719476736 z^9) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (442384067750625 + 124450902576000 z + 94532402764800 z^2 + 150179136307200 z^3 + 1712925142548480 z^4 + 542402905374720 z^5 + 37897113698304 z^6 + 779536564224 z^7 + 4294967296 z^8) Cos[2 Sqrt[z]] + (-1327152203251875 + 435578159016000 z + 52294520678400 z^2 - 225268704460800 z^3 + 1404190322196480 z^4 + 516301353123840 z^5 + 37325950156800 z^6 + 776315338752 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]]))/(24936923717959680 z^(19/4))

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]