Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7161)

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=4, b₁>=-23/4

For fixed z and a₁=4, b₁=-17/4

http://functions.wolfram.com/07.22.03.7161.01

Input Form

HypergeometricPFQ[{4}, {-(17/4), 17/4}, -z] == (1/(208896 z^(13/4))) (2 z^(1/4) (91216125 - 40540500 z + 8814960 z^2 - 1285248 z^3 + 152832 z^4 - 4096 z^5) - Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (-91216125 + 64864800 z - 15301440 z^2 + 2280960 z^3 - 287232 z^4 + 8192 z^5) Cos[2 Sqrt[z]] - 33 (-2764125 + 5651100 z - 2101680 z^2 + 362880 z^3 - 52480 z^4 + 4096 z^5) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (33 (-2764125 + 5651100 z - 2101680 z^2 + 362880 z^3 - 52480 z^4 + 4096 z^5) Cos[2 Sqrt[z]] + 2 Sqrt[z] (-91216125 + 64864800 z - 15301440 z^2 + 2280960 z^3 - 287232 z^4 + 8192 z^5) Sin[2 Sqrt[z]]))

Standard Form

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MathML Form

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