Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7675)

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/07.22.03.7675.01

Input Form

HypergeometricPFQ[{6}, {-(23/4), 15/4}, -z] == (1/(3221913600 z^(11/4))) (4 z^(3/4) (-10854718875 + 5472967500 z - 1162789200 z^2 - 370938240 z^3 + 51344640 z^4 + 3039232 z^5 + 65536 z^6) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((32564156625 - 72243171000 z + 38626988400 z^2 - 10118908800 z^3 - 2500243200 z^4 + 414935040 z^5 + 23592960 z^6 + 524288 z^7) Cos[2 Sqrt[z]] + 10 Sqrt[z] (6512831325 - 5764859100 z + 2354592240 z^2 - 51891840 z^3 - 160033536 z^4 + 319488 z^5 + 327680 z^6) Sin[2 Sqrt[z]]) - Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (-10 Sqrt[z] (6512831325 - 5764859100 z + 2354592240 z^2 - 51891840 z^3 - 160033536 z^4 + 319488 z^5 + 327680 z^6) Cos[2 Sqrt[z]] + (32564156625 - 72243171000 z + 38626988400 z^2 - 10118908800 z^3 - 2500243200 z^4 + 414935040 z^5 + 23592960 z^6 + 524288 z^7) 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]