Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9041)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.9041.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, 15/4}, -z] == (Sqrt[Pi] z^(3/4) (64848554580434625 - 169400305842768000 z + 287467185672576000 z^2 + 613263329434828800 z^3 + 129108069354700800 z^4 + 7983494143672320 z^5 + 181959980482560 z^6 + 1578400481280 z^7 + 4294967296 z^8) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 (4 Sqrt[z] (2069454127104000 - 8735809004047125 z + 13118585359042800 z^2 + 36994649929977600 z^3 + 7980120208650240 z^4 + 496875821137920 z^5 + 11354112000000 z^6 + 98599698432 z^7 + 268435456 z^8) Cos[2 Sqrt[z]] + (-4138908254208000 + 1373977486893375 z + 170981952850800 z^2 + 32279077586246400 z^3 + 7640338477363200 z^4 + 488661967503360 z^5 + 11281005281280 z^6 + 98398371840 z^7 + 268435456 z^8) Sin[2 Sqrt[z]]))/ (618567820325683200 z^(7/2))

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]