Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8287)

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/07.22.03.8287.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, -(19/4)}, -z] == (1/(687465528750 Sqrt[z])) (-4 Sqrt[z] (-13749310575 + 551350800 z - 34594560 z^2 + 3870720 z^3 - 983040 z^4 + 1048576 z^5) Cos[2 Sqrt[z]] - 33554432 Sqrt[Pi] z^(25/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + (316234143225 - 10475665200 z + 518918400 z^2 - 42577920 z^3 + 6881280 z^4 - 3145728 z^5 + 16777216 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]