Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8713)

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`=-5/2

http://functions.wolfram.com/07.22.03.8713.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(5/2), 23/4}, -z] == -((209 (Sqrt[Pi] (2300958069901115625 + 846329405021100000 z + 221584426041888000 z^2 + 64314754043904000 z^3 + 35310061043712000 z^4 - 52150244003020800 z^5 + 15451924149043200 z^6 - 3139438557265920 z^7 + 1448971641815040 z^8 + 101017630801920 z^9 + 1099511627776 z^10) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (766986023300371875 - 68512380406470000 z + 1563205827456000 z^2 + 3866214559334400 z^3 - 3598404009984000 z^4 + 1025782170255360 z^5 - 210779882127360 z^6 + 89405112975360 z^7 + 6300717023232 z^8 + 68719476736 z^9) Cos[2 Sqrt[z]] + (-2300958069901115625 + 1608025869540090000 z + 57838615615872000 z^2 + 12514808265523200 z^3 - 5458185260236800 z^4 + 1311828502118400 z^5 - 260076711444480 z^6 + 84895397314560 z^7 + 6249177415680 z^8 + 68719476736 z^9) Sin[2 Sqrt[z]])))/ (15959631179494195200 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]