Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8sp)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a8sp.01

Input Form

HypergeometricPFQ[{-(13/4)}, {11/2, 23/4}, -z] == (Sqrt[Pi] (2569030373534625 - 7307464173609600 z + 5314519398988800 z^2 - 2208631438540800 z^3 + 981613972684800 z^4 + 661297834229760 z^5 + 46003327598592 z^6 + 865435910144 z^7 + 4294967296 z^8) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-442137563083125 + 338527707663600 z - 138381979357440 z^2 + 54651605299200 z^3 + 40813517144064 z^4 + 2865176248320 z^5 + 54039412736 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + (27931668321375 + 253506395142000 z - 112923616216320 z^2 + 31573134028800 z^3 + 38826418176000 z^4 + 2825489743872 z^5 + 53838086144 z^6 + 268435456 z^7) Sin[2 Sqrt[z]]))/ (881945764429824 z^(19/4))

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]