Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7tp)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.a7tp.01

Input Form

HypergeometricPFQ[{-(17/4)}, {7/2, 11/4}, -z] == (1/(6124213370880 z^(5/2))) (Sqrt[Pi] z^(3/4) (-406586755575 + 1858682311200 z + 6758844768000 z^2 + 1922515845120 z^3 + 134913392640 z^4 + 2887778304 z^5 + 16777216 z^6) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 (4 Sqrt[z] (-10998374400 + 69774070275 z + 402931175760 z^2 + 118647590400 z^3 + 8398675968 z^4 + 180289536 z^5 + 1048576 z^6) Cos[2 Sqrt[z]] + (21996748800 - 33348220425 z + 335503406160 z^2 + 112883811840 z^3 + 8266752000 z^4 + 179503104 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]