Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6893)

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=3, b₁>=-23/4

For fixed z and a₁=3, b₁=-15/4

http://functions.wolfram.com/07.22.03.6893.01

Input Form

HypergeometricPFQ[{3}, {-(15/4), 23/4}, -z] == -((1/(32768 z^(19/4))) (19 (4 z^(3/4) (1895268375 - 437451300 z + 41081040 z^2 - 1584000 z^3 + 20224 z^4) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (-5685805125 + 3478374900 z - 555675120 z^2 + 34404480 z^3 - 834816 z^4 + 4096 z^5) Cos[2 Sqrt[z]] + 3 (1895268375 - 3686482800 z + 1057296240 z^2 - 102896640 z^3 + 4074240 z^4 - 53248 z^5) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (3 (-1895268375 + 3686482800 z - 1057296240 z^2 + 102896640 z^3 - 4074240 z^4 + 53248 z^5) Cos[2 Sqrt[z]] + 2 Sqrt[z] (-5685805125 + 3478374900 z - 555675120 z^2 + 34404480 z^3 - 834816 z^4 + 4096 z^5) Sin[2 Sqrt[z]]))))

Standard Form

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MathML Form

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<ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </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]