Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8399)

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`=7/2

http://functions.wolfram.com/07.22.03.8399.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, -(3/4)}, -z] == (1/(95935039200 z^(5/2))) (-2 Sqrt[z] (7972289325 + 8176707000 z - 12426099840 z^2 + 28813086720 z^3 + 9478537200 z^4 + 630952704 z^5 + 12374016 z^6 + 65536 z^7) Cos[2 Sqrt[z]] - 16 Sqrt[Pi] z^(17/4) (36227354625 + 10037016000 z + 642369024 z^2 + 12435456 z^3 + 65536 z^4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + (7972289325 - 2453012100 z + 21804552000 z^2 - 31699261440 z^3 + 276634828800 z^4 + 79372047744 z^5 + 5120514048 z^6 + 99385344 z^7 + 524288 z^8) 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]