Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8965)

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/07.22.03.8965.01

Input Form

HypergeometricPFQ[{-(21/4)}, {7/2, -(13/4)}, -z] == (1/(1581702202080 z^(5/2))) (2 Sqrt[z] (-948702429675 - 219988969200 z + 21275654400 z^2 - 2426941440 z^3 + 474808320 z^4 - 242221056 z^5 + 1358954496 z^6 + 33554432 z^7) Cos[2 Sqrt[z]] + 8388608 Sqrt[Pi] z^(27/4) (651 + 16 z) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + (948702429675 - 1044947603700 z + 138940401600 z^2 - 13699445760 z^3 + 1966325760 z^4 - 578027520 z^5 + 666894336 z^6 + 16777216 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]