Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7so)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.a7so.01

Input Form

HypergeometricPFQ[{-(17/4)}, {5/2, 23/4}, z] == (4 z^(1/4) (-2348038513445625 - 3130718017927500 Sqrt[z] + 1908247172832000 z^(3/2) - 878950212940800 z^2 - 2590590101299200 z^(5/2) - 205590412984320 z^3 - 7319421096099840 z^(7/2) - 5031155043532800 z^4 + 22910748823388160 z^(9/2) + 1097043195985920 z^5 - 4551289451053056 z^(11/2) - 57460823949312 z^6 + 232620797460480 z^(13/2) + 940597837824 z^7 - 3775276253184 z^(15/2) - 4294967296 z^8 + 17179869184 z^(17/2) + E^(4 Sqrt[z]) (2348038513445625 - 3130718017927500 Sqrt[z] + 1908247172832000 z^(3/2) + 878950212940800 z^2 - 2590590101299200 z^(5/2) + 205590412984320 z^3 - 7319421096099840 z^(7/2) + 5031155043532800 z^4 + 22910748823388160 z^(9/2) - 1097043195985920 z^5 - 4551289451053056 z^(11/2) + 57460823949312 z^6 + 232620797460480 z^(13/2) - 940597837824 z^7 - 3775276253184 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) + E^(2 Sqrt[z]) Sqrt[2 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) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 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) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z])/(382366163675381760 z^(19/4))

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]