Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8115)

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`=-5/2

http://functions.wolfram.com/07.22.03.8115.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(5/2), 1/4}, -z] == (1/82944000) ((-Sqrt[Pi]) z^(3/4) (476974575 - 778734000 z + 755136000 z^2 + 805478400 z^3 + 67829760 z^4 + 1048576 z^5) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 ((-(-41472000 - 12488175 z + 13487040 z^2 + 46609920 z^3 + 4177920 z^4 + 65536 z^5)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (20736000 - 45603675 z + 39329280 z^2 + 49574400 z^3 + 4227072 z^4 + 65536 z^5) 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]