Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a973)

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`=9/2

http://functions.wolfram.com/07.22.03.a973.01

Input Form

HypergeometricPFQ[{-(11/4)}, {9/2, 13/4}, -z] == (1/(4345036800 z^(7/2))) (Sqrt[Pi] z^(5/4) (1206079875 - 2144142000 z + 5277888000 z^2 + 1655808000 z^3 + 90112000 z^4 + 1048576 z^5) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (106444800 - 212595075 z + 251475840 z^2 + 98449920 z^3 + 5570560 z^4 + 65536 z^5) Cos[2 Sqrt[z]] + 4 (13305600 + 106444800 z - 165678975 z^2 + 312607680 z^3 + 102458880 z^4 + 5619712 z^5 + 65536 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]