Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8zb)

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`=-3/2

http://functions.wolfram.com/07.22.03.a8zb.01

Input Form

HypergeometricPFQ[{-(11/4)}, {-(3/2), 21/4}, -z] == (221 (Sqrt[Pi] (204622092675 + 76647740400 z + 21515155200 z^2 + 7649832960 z^3 + 11127029760 z^4 - 5086642176 z^5 + 1291845632 z^6 + 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-204622092675 + 141615825120 z + 4810417920 z^2 + 738017280 z^3 - 331677696 z^4 + 65011712 z^5 + 16777216 z^6) Cos[2 Sqrt[z]] - 4 Sqrt[z] (68207364225 - 5631262560 z + 531336960 z^2 + 745586688 z^3 - 326172672 z^4 + 77594624 z^5 + 16777216 z^6) Sin[2 Sqrt[z]])))/(2886218022912 z^(17/4))

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]