Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6671)

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=2, b₁>=-23/4

For fixed z and a₁=2, b₁=-7/4

http://functions.wolfram.com/07.22.03.6671.01

Input Form

HypergeometricPFQ[{2}, {-(7/4), 23/4}, -z] == (1/(16384 z^(19/4))) (3135 (4 z^(3/4) (675675 - 116820 z + 7200 z^2 - 64 z^3) - Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((2027025 - 3825360 z + 907200 z^2 - 53760 z^3 + 512 z^4) Cos[2 Sqrt[z]] + 6 Sqrt[z] (675675 - 374220 z + 43680 z^2 - 1216 z^3) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (6 Sqrt[z] (-675675 + 374220 z - 43680 z^2 + 1216 z^3) Cos[2 Sqrt[z]] + (2027025 - 3825360 z + 907200 z^2 - 53760 z^3 + 512 z^4) 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]