Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9143)

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`=-11/2

http://functions.wolfram.com/07.22.03.9143.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(11/2), 21/4}, -z] == (221 (Sqrt[Pi] (22209267579206833125 + 6307957655632710000 z + 1281616793525376000 z^2 + 308690496505036800 z^3 + 274391552448921600 z^4 - 63627026654822400 z^5 + 5102919430963200 z^6 - 212069378949120 z^7 + 5141075853312 z^8 - 68719476736 z^9) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-22209267579206833125 + 17381927762187912000 z - 569607463789056000 z^2 + 22717482426777600 z^3 - 4337474703851520 z^4 + 332686216396800 z^5 - 13571425566720 z^6 + 325343772672 z^7 - 4294967296 z^8) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-7403089193068944375 + 1281616793525376000 z - 12945624177024000 z^2 - 18072170894131200 z^3 + 4042873647267840 z^4 - 321560342691840 z^5 + 13316344774656 z^6 - 322122547200 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]])))/ (61444580041052651520 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]