Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8219)

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`=-1/2

http://functions.wolfram.com/07.22.03.8219.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(1/2), 9/4}, -z] == ((-Sqrt[Pi]) (-316234143225 - 5059746291600 z + 26985313555200 z^2 + 102801194496000 z^3 + 29905802035200 z^4 + 2126634811392 z^5 + 45919240192 z^6 + 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-(316234143225 - 533326641120 z + 5077559934720 z^2 + 1754545766400 z^3 + 130286026752 z^4 + 2854223872 z^5 + 16777216 z^6)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-105411381075 + 989484219360 z + 6122367256320 z^2 + 1845325676544 z^3 + 132383440896 z^4 + 2866806784 z^5 + 16777216 z^6) Sin[2 Sqrt[z]]))/ (10511513026560 z^(5/4))

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]