Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8227)

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`=-1/2

http://functions.wolfram.com/07.22.03.8227.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(1/2), 17/4}, -z] == ((-Sqrt[Pi]) (-2348038513445625 - 2504574414342000 z - 2914413863961600 z^2 - 15543540607795200 z^3 + 41449441620787200 z^4 + 94741580847513600 z^5 + 18374124770426880 z^6 + 933288877228032 z^7 + 15113989914624 z^8 + 68719476736 z^9) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-(2348038513445625 + 878950212940800 z^2 - 205590412984320 z^3 + 5031155043532800 z^4 + 1097043195985920 z^5 + 57460823949312 z^6 + 940597837824 z^7 + 4294967296 z^8)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-782679504481875 - 477061793208000 z - 647647525324800 z^2 + 1829855274024960 z^3 + 5727687205847040 z^4 + 1137822362763264 z^5 + 58155199365120 z^6 + 943819063296 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]]))/(26495481450332160 z^(13/4))

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]