Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9957)

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`=-1/2

http://functions.wolfram.com/07.22.03.9957.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(1/2), 19/4}, -z] == ((-Sqrt[Pi]) (5277564317025 + 3612450441600 z + 2223046425600 z^2 + 2634721689600 z^3 - 10538886758400 z^4 + 26979550101504 z^5 + 7993940770816 z^6 + 401579442176 z^7 + 4294967296 z^8) FresnelS[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) (4 Sqrt[z] (1759188105675 + 399949870320 z + 320518598400 z^2 - 825318100992 z^3 + 1602156036096 z^4 + 495025389568 z^5 + 25048383488 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + (-5277564317025 + 2016951496560 z + 200544664320 z^2 - 1082117836800 z^3 + 1301620260864 z^4 + 477082157056 z^5 + 24847056896 z^6 + 268435456 z^7) Sin[2 Sqrt[z]]))/ (11544872091648 z^(15/4))

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]