Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9769)

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`=-9/2

http://functions.wolfram.com/07.22.03.9769.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(9/2), 23/4}, -z] == (209 (Sqrt[Pi] (-6370679826188803125 - 1652933144092230000 z - 291426229261440000 z^2 - 53595628369920000 z^3 - 17150601078374400 z^4 + 13067124631142400 z^5 - 1639796032143360 z^6 + 96105261957120 z^7 - 3285649981440 z^8 + 68719476736 z^9) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-2123559942062934375 + 419792544531360000 z - 2158712809344000 z^2 - 1291355799552000 z^3 + 839029281914880 z^4 - 103708612362240 z^5 + 6046844190720 z^6 - 206158430208 z^7 + 4294967296 z^8) Cos[2 Sqrt[z]] + (6370679826188803125 - 5142458670509160000 z + 254111336414208000 z^2 - 2578348910592000 z^3 + 943983142502400 z^4 - 109018160824320 z^5 + 6214951895040 z^6 - 209379655680 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]])))/(4787889353848258560 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]