Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7667)

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=6, b₁>=-23/4

For fixed z and a₁=6, b₁=-23/4

http://functions.wolfram.com/07.22.03.7667.01

Input Form

HypergeometricPFQ[{6}, {-(23/4), -(1/4)}, -z] == (1/181704600) (4 (45426150 - 189604800 z + 142652475 z^2 + 65856420 z^3 + 7558320 z^4 + 1248768 z^5 - 4096 z^6) - Sqrt[Pi] z^(5/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((986792625 - 1266993000 z - 499086000 z^2 - 54768000 z^3 - 10240000 z^4 + 32768 z^5) Cos[2 Sqrt[z]] + 50 Sqrt[z] (39471705 + 1949220 z - 3330096 z^2 - 591360 z^3 + 20480 z^4) Sin[2 Sqrt[z]]) + Sqrt[Pi] z^(5/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] (-50 Sqrt[z] (39471705 + 1949220 z - 3330096 z^2 - 591360 z^3 + 20480 z^4) Cos[2 Sqrt[z]] + (986792625 - 1266993000 z - 499086000 z^2 - 54768000 z^3 - 10240000 z^4 + 32768 z^5) Sin[2 Sqrt[z]]))

Standard Form

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MathML Form

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45426150 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]