Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7v9)

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`=9/2

http://functions.wolfram.com/07.22.03.a7v9.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, 19/4}, -z] == (Sqrt[Pi] (-2911567756672575 + 11293353722851200 z - 12906689968972800 z^2 + 12515578151731200 z^3 + 16687437535641600 z^4 + 2248412636381184 z^5 + 86895174352896 z^6 + 1131723882496 z^7 + 4294967296 z^8) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (606204368426475 - 753315439902480 z + 632542518316800 z^2 + 1018672592007168 z^3 + 139535817179136 z^4 + 5417796108288 z^5 + 70682411008 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + (-241886151295425 - 271552488938640 z + 177676424190720 z^2 + 929077290086400 z^3 + 135686522732544 z^4 + 5365627355136 z^5 + 70481084416 z^6 + 268435456 z^7) Sin[2 Sqrt[z]]))/ (18851590714687488 z^(15/4))

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]