Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9057)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9057.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, -(17/4)}, -z] == (-2 Sqrt[z] (972728318706519375 - 338800611685536000 z - 6830657493660000 z^2 + 161911881331200 z^3 - 5363540582400 z^4 + 265686220800 z^5 - 21799895040 z^6 + 3523215360 z^7 - 1610612736 z^8 + 8589934592 z^9) Cos[2 Sqrt[z]] - 34359738368 Sqrt[Pi] z^(39/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + (972728318706519375 - 1635771703294228500 z + 99044533658070000 z^2 - 2023898516640000 z^3 + 56317176115200 z^4 - 2258332876800 z^5 + 141699317760 z^6 - 15854469120 z^7 + 4026531840 z^8 - 4294967296 z^9) Sin[2 Sqrt[z]])/(9321498310924800 z^(9/2))

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]