Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8665)

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`=-7/2

http://functions.wolfram.com/07.22.03.8665.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(7/2), 23/4}, -z] == (209 (Sqrt[Pi] (-10847373758105259375 - 3506221820801700000 z - 791372950149600000 z^2 - 192944262131712000 z^3 - 85753005391872000 z^4 + 96850453148467200 z^5 - 19866759620198400 z^6 + 2242456112332800 z^7 - 206995948830720 z^8 + 43293270343680 z^9 + 1099511627776 z^10) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-3615791252701753125 + 484192537158330000 z + 3349726773120000 z^2 - 8153864828928000 z^3 + 6417067268505600 z^4 - 1277999028633600 z^5 + 143514654474240 z^6 - 13416404090880 z^7 + 2692944494592 z^8 + 68719476736 z^9) Cos[2 Sqrt[z]] + (10847373758105259375 - 8064310187843910000 z - 10049180319360000 z^2 - 30141814929408000 z^3 + 8683084608307200 z^4 - 1473960266956800 z^5 + 160003302359040 z^6 - 15220290355200 z^7 + 2641404887040 z^8 + 68719476736 z^9) Sin[2 Sqrt[z]])))/(31919262358988390400 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]