Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8127)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-5/2

http://functions.wolfram.com/07.22.03.8127.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(5/2), 13/4}, -z] == (Sqrt[Pi] (22429729389375 + 30221109072000 z + 112825473868800 z^2 - 109406520115200 z^3 + 44655722496000 z^4 - 17321007513600 z^5 - 9237870673920 z^6 - 444529115136 z^7 - 4294967296 z^8) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-(22429729389375 + 6296064390000 z + 5490944121600 z^2 - 2450061250560 z^3 + 634983874560 z^4 + 552311193600 z^5 + 27531411456 z^6 + 268435456 z^7)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-7476576463125 - 6655839498000 z + 7031689056000 z^2 - 2819358904320 z^3 + 985020825600 z^4 + 572267692032 z^5 + 27732738048 z^6 + 268435456 z^7) Sin[2 Sqrt[z]]))/ (162349763788800 z^(9/4))

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]