Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8661)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.8661.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(7/2), 19/4}, -z] == (11 (Sqrt[Pi] (-21913886380010625 - 9892161876870000 z - 3617704914969600 z^2 - 2143825134796800 z^3 + 3026576660889600 z^4 - 745003485757440 z^5 + 98107454914560 z^6 - 10349797441536 z^7 + 2435246456832 z^8 + 68719476736 z^9) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-7304628793336875 + 41871584664000 z - 238202792755200 z^2 + 204074004234240 z^3 - 48231153008640 z^4 + 6304529645568 z^5 - 673638776832 z^6 + 151397597184 z^7 + 4294967296 z^8) Cos[2 Sqrt[z]] + (21913886380010625 - 13482650261808000 z - 997474194662400 z^2 + 300501984706560 z^3 - 57462169927680 z^4 + 7158292807680 z^5 - 773698093056 z^6 + 148176371712 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]])))/(49873847435919360 z^(15/4))

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]