Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8451)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.8451.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, 1/4}, -z] == (1/(3380568048000 z^(7/2))) (2 Sqrt[z] (-199307233125 - 94032130500 z - 152631864000 z^2 + 775115827200 z^3 + 577663213050 z^4 + 71837095680 z^5 + 2699719680 z^6 + 34734080 z^7 + 131072 z^8) Cos[2 Sqrt[z]] + 2 Sqrt[Pi] z^(17/4) (9382884847875 + 5106331890000 z + 594191347200 z^2 + 21855313920 z^3 + 278855680 z^4 + 1048576 z^5) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - (-199307233125 + 171710847000 z + 43609104000 z^2 - 651229286400 z^3 + 8621663846400 z^4 + 5003209846800 z^5 + 590205189120 z^6 + 21803458560 z^7 + 278659072 z^8 + 1048576 z^9) 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]