Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9623)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.9623.01

Input Form

HypergeometricPFQ[{-(19/4)}, {9/2, 21/4}, -z] == (Sqrt[Pi] (192437069471521875 - 2131610615684550000 z + 3031623986751360000 z^2 - 2515125085304832000 z^3 + 4643307849793536000 z^4 + 1456724031307776000 z^5 + 105703331069952000 z^6 + 2635719424081920 z^7 + 24236500451328 z^8 + 68719476736 z^9) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(-192437069471521875 + 332821192051656000 z - 242359656863385600 z^2 + 224544262440960000 z^3 + 85412074603806720 z^4 + 6457471480627200 z^5 + 163328211025920 z^6 + 1510754746368 z^7 + 4294967296 z^8)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-186361264059807375 + 233537833562140800 z - 186802152856704000 z^2 + 275471541389721600 z^3 + 89870395663319040 z^4 + 6576181251932160 z^5 + 164450204123136 z^6 + 1513975971840 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]]))/ (3728849374701158400 z^(17/4))

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]