Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8311)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.8311.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, 5/4}, -z] == (1/(15397724160000 Sqrt[z])) (Sqrt[Pi] z^(1/4) (7905853580625 + 50597462916000 z + 32125373280000 z^2 + 4792596480000 z^3 + 225533952000 z^4 + 3617587200 z^5 + 16777216 z^6) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (2025794624175 + 1772145118800 z + 287122429440 z^2 + 13887774720 z^3 + 225116160 z^4 + 1048576 z^5) Cos[2 Sqrt[z]] + 4 (279098265600 + 2879294715675 z + 1956912728400 z^2 + 296984378880 z^3 + 14053908480 z^4 + 225902592 z^5 + 1048576 z^6) 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]