Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a98n)

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

For fixed z and a₁=-11/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a98n.01

Input Form

HypergeometricPFQ[{-(11/4)}, {11/2, 21/4}, -z] == (1/(5449239756800 z^(9/2))) (Sqrt[Pi] z^(1/4) (20461145079375 - 35256126906000 z + 20892519648000 z^2 - 8571290112000 z^3 + 8067096576000 z^4 + 1229271859200 z^5 + 37463523328 z^6 + 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (-4438222224975 + 2145612823200 z - 793206247680 z^2 + 440255692800 z^3 + 74696294400 z^4 + 2325741568 z^5 + 16777216 z^6) Cos[2 Sqrt[z]] + 4 (2002865356800 - 2717072386875 z + 1479990204000 z^2 - 604153186560 z^3 + 490705797120 z^4 + 76397346816 z^5 + 2338324480 z^6 + 16777216 z^7) 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]