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

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=-5/4, b_1`>=-11/2

For fixed z and a₁=-5/4, b_1`=5/2

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

Input Form

HypergeometricPFQ[{-(5/4)}, {5/2, 23/4}, -z] == (1/(8589934592 z^(19/4))) (19 (Sqrt[Pi] (-180093375 - 128066400 z - 93139200 z^2 - 283852800 z^3 + 378470400 z^4 + 346030080 z^5 + 16777216 z^6) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-60031125 - 15246000 z - 15966720 z^2 + 20029440 z^3 + 21430272 z^4 + 1048576 z^5) Cos[2 Sqrt[z]] + (180093375 - 64033200 z + 5322240 z^2 + 7249920 z^3 + 20643840 z^4 + 1048576 z^5) Sin[2 Sqrt[z]])))

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]